Invasive species can be heavily influenced by spatial heterogeneity in the landscape through which they are spreading. This heterogeneity may be endogenous (that is, patchiness in the distribution of the invader itself, or heterogeneity in other species due directly to interactions with the invader) or it may be exogenous (such as patchy resources or heterogenous climatic conditions). I will discuss two studies, each dealing with one of these types of heterogeneity. First, I will present a model for spatial spread of an invasive seaweed that suggests different native grazers can have very different effects on invasion success by generating unique patterns of exogenous heterogeneity. This difference is due to the spatial distribution of disturbed patches, which when cleared of native seaweeds become available for establishment by the invader, that are characteristic of different grazers. Second, I will discuss the effects of population asynchrony (endogenous heterogeneity) on population stability and persistence. For this second topic, I will draw on models that are commonly applied to insect populations.