We present here several new results and discuss some viewpoints pertinent to such problems as: (1) the classification of phase transitions in solids, (2) the equations of phase equilibrium and the correct generalizations of the notion of chemical potential, (3) special cases allowing explicit calculation of equilibrium configurations in some systems, (4) the fundamentally new sources of instability in two-phase heterogeneous configurations, and (5) the propagation of small disturbances and free oscillations of the two-phase system in the close vicinity of equilibrium states