I will discuss an approach to the subconvexity problem for L-functions based on period integral formulae and amplification. In particular, I will describe work in progress with Ruixiang Zhang that attempts to prove a subconvex bound for the central L-values of certain families of automorphic forms on Gan-Gross-Prasad pairs of general rank. I will discuss an approach to the subconvexity problem for L-functions based on period integral formulae and amplification. In particular, I will describe work in progress with Ruixiang Zhang that attempts to prove a subconvex bound for the central L-values of certain families of automorphic forms on Gan-Gross-Prasad pairs of general rank.