We describe recent simulations of interstellar and laboratory ices using the 3-D, off-lattice microscopic Monte Carlo kinetics model MIMICK. The simulations indicate that interstellar ices are capable of achieving porous structures, dependent on physical conditions. In some cases, such structures may be filled as they are formed, by mobile/volatile species such as H2 that become trapped in those structures. Simulations of laboratory water-ice deposition using MIMICK suggest that an additional non-thermal diffusion mechanism is required to reproduce the high degree of porosity achieved for experimental ices at temperatures less than ~80 K. This mechanism is related to the deposition process itself. Simulations of temperature-programmed desorption of mixed molecular ices are ongoing. The interstellar models have also recently been developed to incorporate a full gas-phase chemistry, coupled with the grain-surface chemistry.