In several current important problems in different areas of soft matter physics, controversy persists in interpreting the
molecular dynamics observed by various spectroscopies including dielectric relaxation, light scattering, nuclear magnetic
resonance, and neutron scattering. Outstanding examples include: (1) relaxation of water in aqueous mixtures, in molecular
sieves and silica-gel nanopores, and in hydration shell of proteins; and (2) dynamics of each component in binary miscible
polymer blends, in mixtures of an amorphous polymer with a small molecular glassformer, and in binary mixtures of two small
molecular glassformers. We show the applications of calorimetry to these problems have enhanced our understanding of the dynamics
and eliminated the controversies.