One of Rainer Knizia's early creations, Complica started as a very ingenious "inversion" of Connect 4 - pieces don't fall down into the bottom of the grid but are introduced from the side and stay at the open end of the grid pushing all the pieces ahead of them towards the other side. Players can't introduce a piece where the opponent has just played unless it's a life or death situation or the only possible move.
When it was published, though, it was altered to tread more familiar waters, becoming Connect 4 with the ability to put stones on full columns shifting them.
The tactical/strategic gameplay is quite light - players have got to consider when which pieces could meet and build the treasured line of four. Draws can happen, of course, but less than it would seem at first (especially if the game is played in a relaxed way... possibly how it was intended). The variant including diagonal play sharpens the game quite a bit.