The recent strides which have been made in the use of computer simulations to study phase transitions and critical phenomena are reviewed. We describe how the use of a combination of recently developed histogram techniques and sophisticated Monte Carlo simulation algorithms have allowed the determination of the static critical behavior of the d=3 Ising and Heisenberg models with unprecedented precision. We also discuss the study of dynamic critical behavior in simple spin models by both Monte Carlo and spin dynamics methods. Recent estimates for dynamic critical exponents are reviewed including the first high precision estimate for true dynamics.
