Abstract: This talk will provide a brief introduction to cluster algebras, which were introduced by Fomin and Zelevinsky in 2001 and enjoy deep connections to many other areas of mathematics, including Teichmüller theory, Poisson geometry, quiver representations, integrable systems, tropical geometry, Lie theory, and many more. We will use concrete examples to motivate and explain the definition of a cluster algebra and some basic theory. We will then pose some major questions in the theory of cluster algebras and, if time allows, discuss tools that mathematicians have used, or are currently using, to investigate these questions. This talk will not assume any prior knowledge of cluster algebras.