The Thesis revolves around the interaction between projective 2-representations of 2-categories and 2-dimensional topological quantum field theories with defects. On the one hand, the language of projective 2-representations precisely encodes the notion of anomalous TQFT. On the other hand, the language of 2d TQFT with defects allows one to efficiently perform constructions valid for projective 2- representations of arbitrary 2-categories.