Aquaporins and aquaglyceroporins are membrane channel proteins that selectively transport water and small molecules such as glycerol across biological membranes. Molecular dynamics simulations have made substantial contributions toward understanding the permeation mechanisms of aquaporins in atomic detail. Osmotic pressure is the driving force of the transport by aquaporins. The osmotic water permeability of aquaporins can be estimated from equilibrium molecular dynamics simulations by using linear response theory. The relationship between osmotic permeability and channel structure was investigated by the recently proposed p_f-matrix method. In addition to the water transport, other functions of aquaporins and aquaglyceroporins, i.e., glycerol permeation, proton blockage, and gating, have also been extensively studied by molecular dynamics simulations.