We briefly review the basic tenets of the two most popular methods of molecular simulation, molecular dynamics (MD) and Monte Carlo (MC), highlighting their strengths and limitations. As an illustration, two typical examples from the authors' work are presented: first, selected results from equilibrium molecular dynamics (MD) simulation studies of model liquid-liquid interfaces, then characteristic data obtained for bulk water and aqueous solutions at ambient conditions. We demonstrate the two basic types of thermodynamic averages that can be obtained from these simulations: time-independent, or structural, averages and averages involving the evolution of the system in time (often loosely called dynamic).