This volume contains the proceedings of the AMS Special Session on Combinatorial and Geometric Representation Theory, held virtually on November 20-21, 2021. The articles offer an engaging look into recent advancements in geometric representation theory.Despite diverse subject matters, a common thread uniting the articles of this volume is the power of geometric methods. The authors explore the following five contemporary topics in geometric representation theory: equivariant motivic Chern classes; equivariant Hirzebruch classes and equivariant Chern-Schwartz-MacPherson classes of Schubert cells; locally semialgebraic spaces, Nash manifolds, and their superspace counterparts; support varieties of Lie superalgebras; wreath Macdonald polynomials; and equivariant extensions and solutions of the Deligne-Simpson problem.Each article provides a well-structured overview of its topic, highlighting the emerging theories developed by the authors and their colleagues.