Recent progress on the dielectric studies of pure ice and partially crystallized aqueous mixtures are reviewed. Dielectric relaxation of ice has been controlled by preparation methods. This implies that the dynamics of ice seems to be affected by the impurity content in ice crystal. In dilute gelatin-water mixtures with gelatin concentration up to 5 wt%, dielectric relaxation processes of ice have been found, and those behavior depend strongly on gelatin concentration. In partially crystallized aqueous protein mixtures, three dielectric relaxation processes have been found and these are originated from dynamics of uncrystallized water, ice, and hydrated solute molecules.