Thwomps do not seek out or attack the player. They simply jump up and down in an interval from two to five seconds.
Despite this docile nature, they can be dangerous in hallways or other closed areas where you cannot dodge them or in other words, clamped areas.
Thwomps are remarkable for being one of the only enemies that are invincible. They can kill the protagonist in one stomp in most games, but in some, they simply do a large sum of damage. In very rare cases, Thwomps can be destroyed by a power up such as a star man.