We report both experimental measurements and molecular simulations of the melting and freezing behavior of simple fluids in porous media. The experimental studies are for carbon tetrachloride and nitrobenzene in controlled pore glass (CPG) and Vycor. Differential scanning calorimetry (DSC) was used to determine the melting point in the porous materials for each of the glass samples. In the case of nitrobenzene (which has a nonzero dipole moment), dielectric spectroscopy was also used to determine melting points. Measurements by the two methods were in excellent agreement. The melting point was found to be depressed relative to the bulk value for both fluids. With the exception of smallest pores, the melting point depression was proportional to the reciprocal of the pore diameter, in agreement with the Gibbs-Thomson equation. Structural information about the different confined phases was obtained by measuring the dielectric relaxation times using dielectric spectroscopy. Monte Carlo simulations were used to determine the shift in the melting point, T-m, for a simple fluid in pores having both repulsive and strongly attractive walls. The strength of attraction to the wall was shown to have a large effect on the shift in T-m, with T-m being reduced for weakly attracting walls. For strongly attracting walls, such as graphitic carbon, the melting point increases for slit-shaped pores. For such materials, the adsorbed contact layer is shown to melt at a higher temperature than the inner adsorbed layers. A method for calculating the free energies of solids in pores is presented, and it is shown that the solid-liquid transition is first order in these systems.