I will overview recent efforts that strive to characterize both the speed of invasion fronts and the selected states in the wake of invasion, from a conceptual, somewhat model independent point of view. The first part of the talk will be concerned with pulled and pushed fronts and the marginal stability conjecture, focusing on analytical and computational tools for determining wavespeeds. In the second part, I will present some intriguing examples of invasion mechanisms that are based on higher spatio-temporal resonances. This is joint work with Montie Avery and Matt Holzer.