An overview of Kazhdan-Lusztig polynomials I will introduce Kazhdan-Lusztig polynomials and illustrate how they relate to important topics in representation theory, geometry and combinatorics. While I will briefly mention some results from within the past year, the talk will primarily be a survey of known results and open questions. A main goal of the talk will be to describe the connection between Kazhdan-Lusztig polynomials and representations of Lie algebras.