Explore numerical approaches to studying strongly correlated systems in this 39-minute conference talk presented by Steven White from UC Irvine at the APS March Meeting 2014 Fred Kavli Special Symposium. Delve into topics such as exact diagonalization, quantum Monte Carlo, the sign problem, and classification schemes. Examine the concept of entanglement entropy and its monogamy, as well as matrix product states. Discover results for 2D systems and the TJ model, and gain insights into the current state of research in this field. The presentation also covers dynamical properties, the quantum chemistry niche, and further discussion on the sign problem, providing a comprehensive overview of numerical studies in strongly correlated systems.