Invasive species, climate change, and infectious diseases have been identified as significant threats to biodiversity. As such they represent major threats to the earth's life-support systems. An important characteristic of these threats is the speed with which they spread across space. Recent theoretical developments coupled with empirical case studies are beginning to improve our understanding of the factors that determine the rates of spread of invasive species and infectious diseases. The session will be organized to link theoretical and empirical advances in particular subject areas, pairing new theoretical and empirical advances in particular subject areas together, moving from theory to practice and from basic science toward management implications within each subject area. We will begin with new predictive models that take stochastic and nonlinear processes into account. This will be followed by linking theory of spatial spread with empirical data for invasive plants, and by an invasive insect spatial spread and management perspective. Next we will focus on new developments to spread models that incorporate two-sex systems, which again both develop new theoretical advances in estimating and understanding spread rates and present new empirical data including work on insect systems. Finally, we will discuss incorporating a disease and genetic perspective on spatial spread dynamics.