The background here is that last Christmas, I received as a present one of those fancy new side-cutting can openers.
Now, I thought I understood pretty much how the old top-cutting can openers work -- they shove a blade down through the lid, run it around the can, and hey presto, the top of the can falls out. Sure, it's kind of sharp around the edges, and yes, there's usually a sharp lip left inside the can itself, but that's the cost of doing business, right?
Side-cutting can opener, now that's another story. I simply did not understand how a side-cutting can opener was supposed to work. OK, it did, but how?
Answering that question sent me on a search that turned out to be mostly about how cans are sealed, anyway. I found the answer to be very interesting and thought I would share it with you. Oh, and I did figure out how side-cutting can openers work.
Here's the pictorial explanation. This is from a can of pumpkin, left over from making pie for Thanksgiving. (You knew all this would tie together, right?

Canon 300D, Olympus 38mm bellows lens @f/8, stacked at 0.005".

Very briefly, the lid of a standard metal can is formed by a process called "double seaming", which folds the lid and the side of the can around each other to form a five-layered metal sandwich, with some plastic compound stuck between to complete the seal. You can find more detail at this web site and much more information by searching the Web for words like metal cans double seam.
I'm pretty pleased with how well these pictures illustrate how the double seam looks, and how the side-cutting opener gets it apart.
It's interesting to note that although these are fairly deep stacks, most of the time needed to get these pictures went into preparing the specimens.
The challenge is that whenever you cut and grind metal, it forms a burr on the "downstream" side of the grinding action. In a structure like this crimped sandwich, the burr often ends up completely obscuring the layers of metal. What you see here is the result of several iterations -- grind some, remove burr (using an extremely fine-tipped needle under a dissecting scope), grind a little more, remove smaller burr, grind even less, remove even smaller burr, stop when structure is sufficiently clear.
There's a bit of burr showing at the right side of the bottom "V" in the right-hand frame. (I'd like to claim that I left it for illustration, but of course the truth is, I didn't notice it in time to make it go away.)
An amusing exercise... I hope you enjoy!
--Rik
Edit 12/24/2016, replaced obsolete link http://www.dixiecanner.com/1120.htm with current equivalent in the Internet Archive.