  This article first gives a concise introduction to quantum phase transitions,
emphasizing similarities with and differences to classical thermal transitions.
After pointing out the computational challenges posed by quantum phase
transitions, a number of successful computational approaches is discussed. The
focus is on classical and quantum Monte Carlo methods, with the former being
based on the quantum-to classical mapping while the latter directly attack the
quantum problem. These methods are illustrated by several examples of quantum
phase transitions in clean and disordered systems.
