Abstract: In this talk, I will review work on entanglement entropy in many body systems, it's scaling, relation to numerics and possible experimental checks. I will then describe some recent results on effective entanglement hamiltonians in conformal quantum field theories. In particular, I will show how the free fermion entanglement Hamiltonian in 1d can be obtained by solving a Riemann-Hilbert problem and how finite size corrections to the Hamiltonian may be obtained by perturbing around the Riemann-Hilbert solutions, as well as explore subtle difference between the Neveu-Schwartz and Ramond sectors of free fermion fields.