The spread of an invasive species can be modeled by a reaction-diffusion equation that incorporates certain fundamental behaviors of the individuals.  Do they cooperate for better survival?  Do they aggregate?  This talk will be about understanding the classification and behavior of `pushed' fronts (when nonlinear effects, such as cooperation, determine the invasion speed) and `pulled' fronts.  This topic is decades old, but recents years have seen new settings for these questions, as well as simple, yet hidden, new ideas in the most basic cases.  Since I'm a local speaker, I will aim to cover some fun examples in depth.