This dissertation considers questions about the economics of resources exhibiting spatial-dynamic transition processes, specifically, invasive species and wildfires. These topics are increasingly important due to their large damage potentials and the increasing management budgets by governments, but the economics literature has only recently begun to incorporate both space and time into its analysis. The three essays in this manuscript tackle problems using empirics and numerical modelling in order to continue to expand the economic understanding of spatial-dynamic processes. The first chapter empirically analyzes the decision of land developers to build single family homes near lakes invaded with Eurasian watermilfoil, an aquatic invasive plant. A duration model of land conversion is utilized to discover the change in likelihood that a single-family housing unit will be developed after the arrival of Eurasian watermilfoil. The results show a significant decrease in the likelihood that both lakefront and near lake properties will be developed into homes following a Eurasian watermilfoil invasion. This is shown to have a sizable impact on the number of houses constructed near invaded lakes and suggests that uninvaded lakes are most likely being overdeveloped. The second chapter develops a spatial-dynamic model of the optimal control of a general invasive species which is actively spreading throughout a landscape. Along with explicitly allowing the invasion to spread over space, this model permits the population to grow in intensity as well. It is discovered that optimal intensities of invasion vary over space and that ignoring the natural heterogeneity in the landscape leads to suboptimal management decisions. The inefficiency of these decision is shown to increase as the heterogeneity in ecological carrying capacity increases. The model is then applied to the Asian cap invasion in the Mississippi River basin and shows that the current strategy of preventing Asian carp from entering the Great Lakes may be optimal. Overall, this project showcases the importance of recognizing spatial heterogeneity in ecological carrying capacities along with delivering strong evidence that control efforts need to be spatially targeted to most efficiently manage a spreading invasive species. Finally, the third chapter considers the fact that some spatial-dynamic processes, like wildfires, spread at different rates across landscapes that contain a variety of economically valued patches. Spread rates effect the costs of management, while the values of different properties influence the damages associated with a burn. This chapter incorporates these complexities into a spatial-dynamic model of optimal wildfire management and finds efficient solutions for controlling multifaceted fire scenarios. Suppression of wildfires is shown to be more likely in areas where the economic values are spatially clustered, thereby allowing a minimum amount of control to have the maximum benefit. It is also shown that spatial location with respect to the initial ignition location is important in determining optimal control strategies in heterogeneous spread scenarios.