In this talk I will discuss some recent developments in the study of entanglement in 1+1 and 2+0 dimensions quantum field theories. The seminar is divided into two parts, which are self-contained. In the first half I will review results for entanglement dynamics obtained in the scaling limit of the Ising spin chain, by using a form factor perturbation theory. Speculations about thermalization at large times and its absence will be given; this is a published joint work with O. Castro-Alvaredo, M. Lencses and I. Szecsenyi. In the second part, I will explain how genus two partition functions in CFTs with c<1 can be calculated using the conformal bootstrap. Such partition functions appear in the study of the mutual information and negativity and so-far there was no general technique to determine them. If not already in zeitnot, I will discuss two examples: the Lee Yang and the Ising CFT. The second part is an ongoing collaboration with F. Ares.