Accurate calculations in quantum systems where particle interaction effects are important remain one of the major challenges in science. Quantum Monte Carlo (QMC) simulations are often considered as a possible tool in these situations. In condensed matter physics, QMC has been applied to many different problems, including both ab initio calculations of electronic structure and the study of many-body models. I will give an overview of QMC, and discuss leading issues in its theory and applications, including the fermion sign problem. Major efforts have been invested to develop methods to circumvent the sign problem approximately, while maintaining sufficient accuracy for broad classes of problems. I will describe the state-of-the-art, and discuss three recent applications from my group: in quantum chemistry where accurate energetics in molecular systems are needed to predict chemical bonding and reactions; in materials physics when traditional density-functional total energy approaches are not effective; and in cold atoms and optical lattices where QMC is used to predict new phases.