In this talk we introduce the notion of generalized/categorical families of QFTs. These families of theories have a structure which is analogous to the structure of categorical symmetries in Lagrangian QFTs and may be thought of as the family structure that arises upon explicitly breaking such categorical symmetries by deformations of the action. After describing this structure, we will explain the anomalies of these families and their implications. We will then use this structure to study some higher dimensional deformations of 4d N=1 SUSY gauge theories.