I'm an engineer who has 'recovered' from a knife sharpening obsession. I'll share the least obvious elements of the theory and the simplest technique for keeping a kitchen knife sharp, spending just one minute a week.

The thinner the blade's edge and the smaller its angle, the higher the pressure on the material and the easier it is to cut. This high pressure also affects the edge itself. The sharper the knife, the less durable the edge, and at the same time, the higher the pressure it has to withstand. That's why a sharp knife dulls quickly.
It's possible to achieve extreme sharpness, allowing you to 'stick a sword into the bottom of a stream and watch as leaves floating on the water fall apart upon touching the blade', but the cost of equipment and the amount of time spent would be catastrophic.
After cutting the first few sandwiches, the sharpness will become ordinary. In a few days, the knife will no longer be sharp, and in another month it will turn into a 'how can you even cut with this, isn't there a man in the house?''. Therefore, high sharpness is justified for a pocket knife that isn't actually used. For the kitchen, you need sufficient sharpness that lasts for a reasonable number of days and can then be quickly restored.
I propose that the criterion for sufficient sharpness in a kitchen knife is the ability to slice through a sheet of paper with a cutting motion. And I propose that the criterion for ease of sharpening is a time investment of 1 minute per knife.
How Abrasives Work
Sharpening is grinding. At high speeds, abrasives heat the material faster than they grind it. I assume that at high speed, the material simply doesn't have time to yield to the pressure of the abrasive grain. That's why all proper grinding machines are low-speed. Buyers leave angry reviews like 'too fast for grinding' for cheap polishing and grinding machines converted from angle grinders and other high-speed tools.
The lack of need for speed in grinding is the first reason for the relevance of manual sharpening.
The Difference Between Manufacturing/Repairing/Sharpening/Polishing
The knife diagram (Fig. 1) shows the primary bevel, the secondary bevel, and the cutting edge (CE). The primary bevel is needed to create or renew the secondary bevels by grinding a smaller area. The secondary bevels are needed to create or renew the CE by grinding an extremely small area.
Creating the primary bevels is part of knife manufacturing, done with a powerful grinder using a coarse, large-area grinding belt.
Creating or renewing the secondary bevels is knife repair, an operation to fix blade damage. Thanks to the primary bevel, the area of the secondary bevel is small, and a small grinding machine (mini-grinder, drill with a grinding attachment, etc.) with a medium abrasive is sufficient for repair.
Creating or renewing the CE is sharpening. Thanks to the secondary bevels, an extremely small area needs to be ground (CE width is about 0.1 mm, see Fig. 2), and even manual grinding with a fine abrasive forms a new CE quickly. And since a fine abrasive is used, the knife material is consumed very slowly, and the knife's geometry remains unchanged even after many sharpenings. This is the second reason for the relevance of manual sharpening.

Experimenting with types of abrasives, I went to extremes; I tried sharpening knives with polishing compounds, polishing the CE. And I found out that polishing does indeed polish the metal, it works especially well for polishing the primary bevels with a 3M Trizact 3000 wheel mounted on a cordless drill. But polishing doesn't sharpen, although it might seem like it should.
In search of the perfect sharpening machine, I tried six different grinders (two mini-grinders, three disc grinders, and a cordless belt sander). In the end, I settled on a belt sander with a P320 abrasive belt, which I only use to renew the primary bevels, without trying to sharpen.
So, I repair knives with a belt sander; I polish the primary bevels with an abrasive wheel; and I sharpen with a honing steel. However, my own knives only require sharpening.
Can you do without repairs?
Minor damage to the CE is ground away after a few sharpenings. Major damage is difficult to fix by sharpening; it requires renewing the secondary bevels, i.e., repairing the blade.
The knife's 'friends,' which increase the interval between repairs, are wooden or plastic cutting boards and knife storage systems (Fig. 3).

An example of an 'enemy' is the glass butter dish shown in Fig. 4, whose edges damage the blade with every use.

Sharpening/Repair a la 'Service Center'
Economy-class commercial sharpening services manage to combine sharpening and repair, quickly sharpening a batch of knives in various states of disrepair.
A mechanized coarse-grit grinding wheel works quickly, removes large areas, and renews the secondary bevels at a standard angle. The cutting edge on such a knife will be the continuation of the renewed secondary bevels. A coarse abrasive doesn't promise sharpness; but since the secondary bevel angle 2β is less than the recommended CE angle 2α, such an edge is sharp enough. And the 'saw-like' edge created by the coarse grit makes the cut more 'aggressive'.
A normal CE at an angle of 2α is re-established after such a repair with the very first independent manual sharpening.
The main advantage of sharpening at 'service centers' is the automatic repair of the cutting edge. The main disadvantage is that you have to hand over all your knives in a batch and wait a couple of days. Also, a lot of metal is removed from the knife, and with regular sharpening, the knife will turn into an awl.
Factory Sharpening
Expensive knives are sharpened at the factory on a machine with several stones of progressively finer grit, and then polished. This results in a very beautiful, polished secondary bevel that serves as the cutting edge.
Sharpening Jigs
Sharpening jigs, such as the 'Zhuk' sharpener (see Fig. 5), allow you to clamp the knife and set the abrasive at the desired angle. Then, you are supposed to move the abrasive along the cutting edge, constantly flipping the knife to grind down the resulting burr and changing abrasives from coarse to fine, which allows you to get a sharp knife in an indecently long amount of time. I bought this sharpener, gained the necessary experience, and gave it to a friend.

My own experience and studying specialized forums led me to the opinion that such jigs allow for restoring the factory sharpening, where the secondary bevel acts as the CE. The method allows for a very wide, even, and if desired, polished and very beautiful CE (Fig. 6). Its width can be several millimeters, which corresponds to a grinding area an order of magnitude larger than necessary.

(image from the 'MyRavei and Tsaplya Sharpening Systems' forum)
The size of the area being ground entails an order of magnitude more grinding time and corresponding abrasive consumption. But it's still the edge that cuts; and when that edge dulls, you'll have to grind down a huge area again. For a work knife, this is extremely irrational. But for sharpening expensive and rarely used 'shelf queen' knives, especially by a master, the method is justified — it's beautiful.
The beauty and high cost of the solution create a market, a competition of authorities, dialogues, and a set of values within the sharpening subculture from which it's not so easy to escape. Even I, an engineer, spent over ten thousand rubles just selecting 'prestigious' abrasives before I realized I was heading in the wrong direction.
The epiphany came after watching an hour-long lecture about the difference between two little-known types of Japanese knife steel. While talking, the author was simultaneously sharpening a knife, and at the end, he showed how his incredibly beautiful, insanely expensive knife cut paper not with a slicing motion, but with a mere touch. And then I decided to go in a different direction — to find the optimal way to regularly sharpen kitchen knives.
The Role of Sharpening Angles
There are no substantiated criteria, only legends that say the sharpening angle for Japanese knives is 15°, for European kitchen knives it's from 18° to 22° depending on the load on the knife and the desired time between sharpenings. Hatchets for chopping bones are sharpened at angles of 30° and higher.
The role of sharpening jigs is to maintain a constant sharpening angle during grinding. But what if the angle is held by hand and 'wanders'?
Figure 7, on the left, schematically shows the shape of the CE when grinding at a target angle α, with an instability of the grinding angle in the range of ±Δα. It can be seen that the CE has acquired a 'convex' shape, and the final sharpening angle, i.e., the apex angle, turned out to be α + Δα.

A convex edge is stronger and lasts longer. A pronounced convex CE, as in Figure 7 on the left, is good for a splitting maul designed for huge loads.
Experiments with an electronic angle gauge show that a reasonable and even somewhat pessimistic inaccuracy of setting the angle by hand relative to the target is ±2°. With a base angle of 18°, this error results in a convex edge with an apex angle of 20° — ideal for a kitchen knife. The actual shape of the resulting convexity is shown in Figure 7 on the right — it's so slight that it's almost invisible.
Types of Honing Steels
The material of the honing steel must be an order of magnitude harder than the steel being ground. Diamond honing steels should theoretically work well, but in practice, most of them have only a thin coating of diamond dust that wears off quickly.
Steel honing steels are unsuitable. I tried an expensive steel honing steel from a well-known 'knife' brand and was surprised that it works an order of magnitude slower than a ceramic one.
Ceramic honing steels work well if they have a smooth surface. I most like a 'ruby ceramic' honing steel I bought in Russia, which suspiciously resembles VK 94-1 corundum ceramic. It has a perfectly smooth, very durable, and excellent grinding surface.
Honing Steel Technique
The honing steel most favorably combines all the principles of sharpening.
The smaller the contact area between the abrasive and the steel, the higher the pressure and the faster the grinding. A honing steel is round in cross-section, its 'contact patch' area with the steel is practically zero, and even without pressure, the pressure in the contact patch is enormous. This allows even a smooth honing steel to work effectively.
A dark deposit forms on the honing steel during use. This deposit is ground-off steel and evidence of effective grinding. It can be washed off with a dish sponge and detergent.
Honing steels are held in different ways. I rest the honing steel at the required angle on a support and guide the knife along the steel with the edge leading, from the heel of the blade to the tip (Fig. 8).

I designed a paper template for the 18° angle of the honing steel and the knife (Fig. 9).

Initially, I planned to develop a template for a 3D printer with a rigid honing steel holder, but I realized that regular printers are several orders of magnitude more common, and a paper template would be several orders of magnitude more useful.
Calculating the folds for an A4 sheet to assemble the template into a stable pyramid was not easy — it was almost an Olympiad-level problem. But in the end, even if the printer printed the template not parallel to the paper edges, if you fold along the fold lines, the top edge of the pyramid is oriented to the support at an angle of exactly 18°.
The second goal I managed to achieve is that the template is assembled from a printout on only one side of the sheet (Fig. 10), the instructions are right on the template, and its necessary elements are visible during assembly.

The 18° angle was chosen as optimal. A realistic error of ±2° with an unsteady hand will result in a final sharpening angle of 20°, which is good. An extremely unsteady hand, wandering within, for example, ±4°, will give a sharpening angle of 22°, which is good for infrequent sharpening. Accidentally or intentionally reducing the base angle to 16° with an angle-holding inaccuracy of 2° will give a final angle of 18°, which initially seems sharper but will soon become the same as at 20°. In total, it works out well for a kitchen knife no matter how you look at it.
You can download the template at this link: https://disk.yandex.ru/i/4aaAN34AdlezhA.
Since the honing steel is smooth, you can guide the blade edge-first onto the abrasive — this minimizes burr formation. But since a small burr still forms, it is removed by grinding the other side of the CE, and then vice versa. To avoid chasing the burr back and forth, you need to gradually reduce the number of passes.
Life hack: to protect the table or tablecloth from cuts, rest the honing steel on a cutting board at the edge of the table.
In my experience, the optimal pattern is: 20 passes on one side and 20 on the other, then 10 and 10, then 5 and 5, and finally 2 and 2. This is sufficient for regular sharpening. If it doesn't cut paper cleanly enough, repeat.
Life hack: listen to the character of the steel hissing on the ceramic, and feel this hissing with your hand. When the cutting edge is formed, the sound and the feeling in your hand will change. After a while, you'll be able to hold the angles by sound, and also tell by ear when the necessary sharpness has been achieved.
If you have to sharpen someone else's knives, it's advisable to practice the cutting motion beforehand to make it look impressive, and to say, '— Razor sharp!' so that the owner is pleased.