In this talk, we consider Hankel operators, with locally integrable symbols, densely defined on a family of Fock-type spaces whose weights are C3-logarithmic growth functions with mild smoothness conditions. We characterize the compactness and Schatten class membership of Hankel operators. Besides, we give characterizations of the Schatten class membership of Toeplitz operators with positive measure symbols for the small exponent 0 < p < 1.