The second half of the last century saw exciting developments in formulating mathematically rigorous yet physically well founded theories for irreversible thermodynamics in a continuum mechanics framework. The development took place within communities with widely different scientific backgrounds and motivations. In general, two divergent schools existed (and possibly exit): one of them having its roots in the works of I. Prigogine and S. R. de Groot, and the other initiated by C. Truesdell, B. D. Coleman and W. Noll. The former group took as their starting point, the Gibbs relation, where they assumed that even in the out of equilibrium situation, concepts like entropy are meaningful, if only locally, and can be expressed as functions of the state variables.