Topological data analysis (TDA) is a field which combines topology, geometry, statistics, and computer science to answer questions about data through shape analysis. Taking from algebraic topology, for any given data set, one can construct simplicial complexes and compute topological invariants. In this talk, I plan to give an overview of the tools commonly used in TDA and talk about some of my favorite applications including in cancer research, neuroscience, and population biology. If there is enough time I will also talk about useful software that exists for you to apply these tools too!