This talk aims at giving an introductory overview on studies of different systems which could all be considered as examples of matter under extreme conditions. These range from ultra-dense hadronic matter in compact stars to chirally imbalanced plasmas at high temperature and their applications to condensed matter, heavy-ion collisions and early universe physics. The properties of these systems can be characterized by using a variety of different (and often complementary) methods and applications of thermal quantum field theory, providing an excellent playground for theoreticians who don’t mind getting their hands dirty and can cope with the eternal frustration of dealing with infrared and ultraviolet divergencies.