Twisty puzzles are the encompasing term for puzzles like the Rubik's Cube, and many others with many different shapes. I spent my entire childhood and most of my adult life uninterested in these puzzles, probably because I knew the iconic Rubik's 3x3x3 was difficult to learn and I have Attention Deficit Disorder. At age 52 I did a web search for activities to keep my mind fresh and active while aging. Among other things, solving puzzles was one method. I decided to interpret that as Rubik's type puzzles, so I set off to dip my toe in the twisty puzzle waters.
I still assumed the 3x3x3 would be too much for me, so I ordered a 2x2x2. I'm not interesting in actually figuring them out on my own. I'd rather just learn the methods already discovered, and then just solve them over and over to exercise my mind. After receiving my 2x2x2 I started watching how-to-solve videos and began working on my puzzle. The 2x2x2 is deceptive in that it's so small so a non-puzzler (like myself at the time) might think it's nearly trivial to solve, but it actually has several steps that need to be memorized to solve it consistently. I learned it, solved it a few times, and that awoke in me an interest in looking into other twisty puzzle shapes.
Just 14 days after ordering my first puzzle, the 2x2x2, I did something really crazy. I ordered what would end up being one of my wildest twisty puzzles, the Axis Cube, which is a shape mod of the iconic 3x3x3 cube. A shape mod means that the puzzle operates like another established puzzle, but movements cause the overall shape to start looking very weird, which can significantly add to difficulty in solving. For example, after scrambling a 3x3x3 shape mod, it could like like some kind of weird fractured crystal with spikes jutting out. When I bought this I didn't even own a 3x3x3 and had no intention to. I got it just because it looks cool.
Five days after ordering the Axis I ordered the Pyraminx. I played with these as a kid but never tried to learn them. As an adult I learned it right away and it's actually pretty easy and fun to solve.
Eight days after ordering the Pyraminx I stumbled upon the Skewb. The look of it fascinated me and I had to have it. I learned it right away and it still today remains one of my favorites.
I can't keep describing every puzzle I've bought because I probably have at least fifty; I should count them sometime. I suppose when I write more I'll make a list of my top five or so.