We focus on the various aspects of the physics related to the stability of proteins. We review the pure thermodynamic aspects of the response of a protein to pressure and temperature variations and discuss the respective stability phase diagram. We relate the experimentally observed shape of this diagram to the low degree of correlation between the fluctuations of enthalpy and volume changes associated with the folding-denaturing transition and draw attention to the fact that one order parameter is not enough to characterize the transition. We discuss in detail microscopic aspects of the various contributions to the free energy gap of proteins and put emphasis on how a cosolvent may either enlarge or diminish this gap. We review briefly the various experimental approaches to measure changes in protein stability induced by cosolvents, denaturants, but also by pressure and temperature. Finally, we discuss in detail our own molecular dynamics simulations on cytochrome c and show what happens under high pressure, how glycerol influences structure and volume fluctuations, and how all this compares with experiments.