Polymer phases can be described in the same way as phases in other condensed matter using a number density operator and its correlation functions. This description requires the understanding of both symmetry operations and order at different atomic and molecular levels. Statistical mechanics provides a link between the microscopic description of structure and motion and the macroscopic thermodynamic properties. Within the limits of the laws of thermodynamics, polymers exhibit a rich variety of phase transition behaviours. By definition, a first-order phase transition in a temperature-pressure ensemble describes a transformation which involves a discontinuous change of all the thermodynamic functions but the Gibbs free energy at the transition temperature. Higher-ordered phase transitions are classified as critical phenomena. Of special interest is the role of metastability in phase and phase transition behaviours. A classical metastable state possesses a local free energy minimum, but it is not at the global stable equilibrium. Further, the existence of circumstantial metastability need to be invoked based on the constraints of size, dimensionality, order and symmetry; examples include polymorphism, mesophase concepts, crystal size, and thin film effects. Metastable behaviour is also observed in phase transformations that are impeded by kinetic limitations along the pathway to thermodynamic equilibrium. This is illustrated in structural and morphological investigations of crystallization and mesophase transitions, liquid-liquid phase separation, vitrification and gel formation, as well as combinations of all such transformation processes. In these cases, the metastable state often becomes the dominant state for the entire system, and is observed over a range of time and size scales. This review will describe the general principles of metastability in polymer phases and phase transitions and will provide illustrations from current experimental works in selected areas together with raising so far unaddressed conceptual issues of wider applicability to phase transformations in general.