Geometric representation theory has revealed a deep connection between geometry and quantum groups suggesting that quantum groups are shadows of richer algebraic structures called categorified quantum groups. Crane and Frenkel conjectured that these structures could be understood combinatorially and applied to low-dimensional topology. In this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. We will also survey the applications of this theory including a new grading on blocks of the symmetric group and Webster's recent work categorifying Reshetikhin-Turaev invariants of tangles.