Abstract Nuclear matter is discussed under extreme conditions: Under high pressure and high temperature. The present status of pion condensation and Lee-Wick condensation is reviewed. Although one finds condensation at relatively low densities, if the pion or the σ propagator is calculated in nuclear matter in the random phase approximation the inclusion of the bubbles in bubbles shields against π and σ-condensation by the same mechanism which induces the condensation. Thus π and σ-condensation shields against π- and σ-condensation. Furthermore the critical temperature and critical density for the formation of quark matter is discussed. A high temperature and a high enough density can be reached by high energy collisions betweem two heavy nuclei. If one increases the temperature in the interaction region of the collision between two heavy ions one expects first to reach a “limiting temperature” with increasing bombarding energy of the heavy ions. In the interaction region (“fire ball”) more and heavier hadrons are produced and the bombarding energy is not any more going into an increase of the temperature. But if one increases farther the energy imput, hadronic matter starts to evaporate into a quark-gluon plasma. This should happen at a temperature of about 180 MeV (2.10 12 degrees Kelvin). Possible fingerprints of such a quark-gluon plasma are discussed.