In the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble.