Recently there has been new progress in computing a class of observables in N=4 supersymmetric Yang-Mills theory in four dimensions at finite 't Hooft coupling, ranging from correlation functions of "baryonic" operators to leading instanton effects at large N. All those examples share two common features: 1. At weak coupling, they can be computed by an overlap between a matrix product state and an eigenstate of the Hamiltonian of an integrable 1+1d spin chain. 2. Using AdS/CFT, they can be mapped to so-called g-functions on the string worldsheet and can be computed exactly as a function of 't Hooft coupling. After explaining the basic ideas, I will showcase several applications.