The name is a bit misleading. I thought Tetravex would be something like Tetris. It's really quite unrelated. Since I am an English major, I can use context clues to extrapolate the meanings of words; I've heard the prefix tetr- in two contexts, namely Tetris and Tetravex. I'm going to guess that it means '4'. In Tetris, each piece consists of four blocks. Tetravex, while being nothing at all like Tetris, uses as pieces squares divided into four sections. See? It makes perfect sense.
Otherwise, I have no idea what tetr- means. But that's not important, is it? You want to hear about the game. Barring that, I want to tell you about the game. And use italics as much as possible. Anyway, Tetravex is for fans of Sudoku, I think. It's not a real-time puzzle game, it's a timed logic-puzzle. Each square is divided into four sections, each of which has a number. Squares can only be placed on the play-grid next to pieces whose numbers match.
It's a game that grows exponentially more difficult, as you increase the play-grid size, which actually seems like an obvious thing to say. 2x2 is ridiculously easy. 3x3 is for fun but quick gaming. 4x4 and up (it maxes out at 6x6) is for training your brain, I think. At that level it really does play out something like Sudoku.
Basically, there are two grids. At the start of each game, one is empty, and one is randomly filled with square pieces that are divided into four sections. You have to drag them from the filled one to the empty one, until you have emptied the filled one and filled the empty one, if I can describe this game in as redundant terms as possible.
I haven't quite gotten a real strategy for this one yet, but I like to start with a piece that has at least one side that matches no other pieces on the board, and build from there. This tends to be less possible in the larger grids, but at 3x3 it at least gives me something to go with. If I were the type of person who enjoyed these things, I would probably just solve the damn thing in my head before I moved the first piece, but I like to interact with my interactive entertainment. If I wanted to stare at something, I'd watch more episodes of Scrubs.
In short, Tetravex is another decently conceived and implemented game that I find not very much fun, even at its most fun degree of difficulty. It scales fine (I don't know why I keep mentioning that, but at this point, it almost seems like I have to). It has a 'Hint' feature, and the option to have the computer solve the puzzle for you, if you get totally stuck (I can't imagine that ever happening; you can just brute-force them out if worst comes to worst). And it's got a high-score list that differentiates between each of the available grid-sizes, with the time it took you to solve the puzzle serving as your score.