Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector space" with additive categories. Khovanov-Lauda-Rouquier algebras, or quiver Hecke algebras are introduced for the categorification of quantum algebras. We will give a survey of recent developements in the categorical representation theory.
