Plant-animal mutualistic networks sustain terrestrial biodiversity and human food security. Global environmental changes threaten these networks, underscoring the urgency for developing a predictive theory on how networks respond to perturbations. Here, I synthesise theoretical advances towards predicting network structure, dynamics, interaction strengths and responses to perturbations. I find that mathematical models incorporating biological mechanisms of mutualistic interactions provide better predictions of network dynamics. Those mechanisms include trait matching, adaptive foraging, and the dynamic consumption and production of both resources and services provided by mutualisms. Models incorporating species traits better predict the potential structure of networks (fundamental niche), while theory based on the dynamics of species abundances, rewards, foraging preferences and reproductive services can predict the extremely dynamic realised structures of networks, and may successfully predict network responses to perturbations. From a theoretician's standpoint, model development must more realistically represent empirical data on interaction strengths, population dynamics and how these vary with perturbations from global change. From an empiricist's standpoint, theory needs to make specific predictions that can be tested by observation or experiments. Developing models using short-term empirical data allows models to make longer term predictions of community dynamics. As more longer term data become available, rigorous tests of model predictions will improve.