Modelling seed dispersal by animals seems straightforward; we need a way to keep track of the position on the animal through time and a clock for how long seeds travel with it. Mathematical models show how changing seed retention parameters can result in very different seed dispersal kernels, including fat-tailed ones. When movement is more realistic, in the sense that it is tied to the spatial distribution of resources, agent-based models result in both seed consumption and dispersal kernels varying according to the neighborhoods of focal plants. In general, agent-based models are built in ways that lead to overparameterization and poor predictive capacity. Considering several emergent properties that one wishes to capture and building a hierarchy of models varying in complexity should improve our understanding of the important mechanisms behind particular patterns. Progress in hierarchical data analysis tools allows fitting joint-species models in which species-level movement and foraging parameters are modelled as a function of species traits and their phylogenetic relationships. Overall, there has been great progress in data collection and modelling of seed dispersal by animals but we still need a better understanding of seed retention times, and of how bird physiology influences fruit choice. Further improvements in our ability to understand and predict seed dispersal by animals would probably also require considering individual personalities, as well as within and among species interactions. As our capacity to collect data bring us into the realm of big data and big models, important progress in mechanistic modelling of seed dispersal by animals should be achieved by close collaborations merging ecology, behavior, physiology, mathematics, computation and statistics.