There has been phenomenal recent progress in computing entanglement and Renyi entropy in conformal field theories with pure gravity duals. In an effort to elucidate the intersection of holography, entanglement and the fundamental structure of CFTs, we extend these methods to more general CFTs and their gravity duals. We focus mostly on AdS_3/CFT_2. First, we work in the realm of higher spin holography, by computing ground state entanglement and Renyi entropy in certain classes of holographic 2d CFTs with higher spin symmetry. This involves a precise match between CFT and higher spin gravity calculations, performed at both leading and next-to-leading order in large central charge (small Newton's constant). We will also present results on entanglement entropy in 2d CFTs with a gravitational anomaly. Time permitting, we will discuss purely field-theoretic methods for computing Renyi entropy in generic CFTs in any spacetime dimension, and apply them to the 3d O(N) vector model coupled to a Chern-Simons gauge field at large N.