The structure of entanglement can yield new physical insights into many-body quantum systems. Here, I’ll describe key properties of the entanglement entropy of CFTs in 2+1d. In particular, we’ll see that sharp corners in the entangling surface contribute a regulator-independent function that depends non-trivially on the corner opening angle. I’ll argue that in the smooth limit this function yields the 2-point function of the stress tensor. This sheds light on recent cutting edge simulations of the quantum critical Ising, XY and Heisenberg models. I’ll also present a new lower bound for this function. I will then generalize to Rényi entropies, which yields a simple procedure to extract the thermal entropy using corner entanglement of the groundstate alone. Connections will be made to CFTs in 1+1d and 3+1d, as well as to Lifshitz theories.