This talk will begin by explaining a few avatars of the notion of a family of TQFTs parameterized by a certain space. I will then explain the connection with symmetry, anomalous symmetries, and projective TQFTs. The second half will be primarily concerned with the three-dimensional setting. This will involve the Morita theory of fusion categories along with their higher groups of symmetries and the homotopy theory of these higher symmetries. (This is my dissertation defense.)