I will discuss the difficulties inherent in the classical simulation of quantum many-body systems and provide an overview of the state-of-the-art algorithms developed for this task, focusing on tensor network based approaches. By exploiting the boundary laws for entanglement entropy scaling found in local systems, tensor network states can provide efficient representations of ground state wavefunctions in many interesting classes of quantum systems. I will review some of the successes of the tensor network program, and outline the open challenges that remain.

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