Thwomps have been around in the Mario games since Mario Bros. 3. In Super Mario 64, Thwomps return in a much different fashion, and look more like they did in Super Mario Kart. These Thwomps are square-shaped, dark sky blue-colored and have no spikes. They, as before, are impossible to destroy and serve as obstacles throughout the game. This time around, though, Mario could also use Thwomps to his advantage by jumping on top of them to reach higher areas or unreachable points. Thwomps were especially featured in Whomp’s Fortress, which also featured new Thwomp-like creatures known as Whomps.
Grumpy Thwomp by Mastermind777 (right on picture)
Info from Mario Wiki