We investigate the kinetics of chiral phase transitions in quark matter. We discuss the phase diagram of this system in both a microscopic framework (using the Nambu-Jona-Lasinio model) and a phenomenological framework (using a Landau free energy). Then, we study the far-from-equilibrium coarsening dynamics subsequent to a quench from the chirally-symmetric phase to the massive quark phase. Depending on the nature of the quench, the system evolves via either {\it spinodal decomposition} or {\it nucleation and growth}. The morphology of the ordering system is characterized using the order-parameter correlation function, structure factor, domain growth laws, etc.

40 pages with 14 figures, references added, introduction and discussions extended; version to appear in Nuclear Physics A