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For quantum systems with many interacting particles, the lowest energy states, aka "ground states", store rich information about physical behavior. Extracting information about the structure of these ground states even for just 1 spatial dimension is in general a very hard problem. A restricted class of ground states, called "matrix product states", are relatively simple ground states which capture interesting phenomena in a variety of models. They are often reasoned about diagrammatically, by way of tensor network notation, a graphical toolkit of growing popularity in quantum many-body physics and quantum information theory. In this expository talk, we introduce tensor network notation and work up to matrix product states. If time allows, we will discuss some recent results for an interesting class of models described by these matrix product states.