CFTs Old and New from the Bootstrap

The conformal bootstrap gives a powerful and rigorous way to learn about strongly-interacting conformal field theories and critical phenomena. I will discuss recent results from the conformal bootstrap in 3 and 4 dimensions, making precise predictions in known CFTs such as the 3D Ising, O(N) vector, and Gross-Neveu models, as well as giving exciting evidence for possible new conformal field theories.