  We review different descriptions of many--body quantum systems in terms of
tensor product states. We introduce several families of such states in terms of
known renormalization procedures, and show that they naturally arise in that
context. We concentrate on Matrix Product States, Tree Tensor States,
Multiscale Entanglement Renormalization Ansatz, and Projected Entangled Pair
States. We highlight some of their properties, and show how they can be used to
describe a variety of systems.
