A comprehensive review of solid-liquid phase transition studies based on molecular computer simulations is given. Topics such as reliable characterization of phase transition temperature, heating and freezing rates used in simulations, the significance of the initial configurations in solid water clusters, polymorphic solid-solid transitions masking the melting point and the question of reliability of current water interaction potentials, originally developed to study liquid bulk water are discussed. Results from melting and freezing studies are discussed, including with the presence of applied electric field. Several simple physical models relating the melting temperature to cluster size and thereby to the number of molecules in the clusters are compared to simulation results. The large bulk of simulations carried out using SPC/E and TIP4P water models allow a systematic comparison.