Let E/F be a quadratic extension of number fields. A cuspidal representation pi of GL_n(A_E) is distinguished by the quasi-split unitary group wrt E/F if and only if pi is Galois invariant. This result was recently proved by Jacquet using the relative trace formula which he developed. I will discuss refinements of this result and extension to other unitary groups. Also, I will address the local analogue of this question: what can be said about the space of functionals invariant under a unitary group. Joint work with Brooke Feigon and Omer Offen.