Heavy particles provide an ideal window for new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe also non-relativistic particles propagating in a medium. After introducing the general concepts underlying modern effective field theories for non-relativistic particles in a thermal bath, I discuss them on the examples of (a) heavy Majorana neutrinos colliding with a hot plasma of Standard Model particles in the early universe and (b) quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.