My personal preference is to sharpen chisels and plane blades with Japanese waterstones, carving chisels with a leather strop, gouges with a contoured leather strop or contoured felt wheel chucked in a grinder, moulding plane blades with slipstones, and carving knives with ceramic stones.
And there are more methods available than just these.

After hearing Mike Dunbar's presentation at the WIA Conference, I remembered an old drawknife I had purchased (and never sharpened) when I was new to woodworking. Following is how I sharpened this tool, but there are other ways to do it.*
First, sandpaper was used to remove the fine layer of rust that had covered the blade from sitting unused in my basement for 16 years.
A drawknife cannot easily be sharpened by holding the blade and moving it along a stone, as you would a plane bl ade. Instead, it's easier to keep the drawknife stationary and take the stone to it.
So, I used an 80 grit diamond stone to "scrub", in a circular pattern, the flat side of the blade. You can see the swirl marks in the photos.
Note: Please be careful with this sharpening technique. It's very easy to slip and cut yourself. (Don't ask me how I know this.)
A 600 grit ceram

The blade was very dull, so a circular motion was a fast way to remove steel. But I changed to carefully sliding the stones back and forth as the blade became sharp.
The same technique was used to sharpen the curved side of the blade, except that I w

This drawknife can benefit from a little more sharpening to remove scratch marks, but I took it for a test drive anyhow. It worked great and rounded the edge of a piece of cherry effortlessly. And after 16 years, I'm finally able to put this fun-to-use handtool to the work it deserves.
*Mike Dunbar uses sandpaper wrapped around a block of wood to sharpen his drawknives.