Heat and rut suppressants are usually pills or a shot that can suppress heats and/or ruts. You won't take both - just the one that's applicable for your gender. Think of these as birth control - they typically lessen the pain and the frequency of ruts and heats. Often they also provide birth control for the user.

In most universes, taking suppressants for too long a time will permanently damage your cycle or reproductive organs. A common plot device is to have the suppressants fail, or the protagonist forgets to take them, which brings on the onset of a very strong heat or rut.