The technique of positron annihilation as applied to the study of phase transitions in molecular substances and polymers is reviewed. The emphasis is on the formation and annihilation of positronium atoms in condensed media. The annihilation rate of ortho-positronium in a medium is highly sensitive to microscopic structural changes which usually occur during phase transitions. The positron method is particularly valuable for the study of solid-solid phase changes, including the glass transition in polymers.