This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference \""Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification\"", held on the occasion of Chari's 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari's significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including:\nString diagrams and categorification\nQuantum\n\nInteractions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification\nIn honor of Vyjayanthi Chari on the occasion of her 60th birthday\nFree UK delivery on this;