Many dynamic phenomena can be modeled as a diffusion process. For my dissertation, I study diffusion processes in the area of sustainability, such as how wildlife spreads over a fragmental landscape and how fish spread within a river network, and try to answer two important questions. 1) How to shape the diffusion by using a limited amount of resources, for example how to maximize the spread of birds by preserving a limited number of landscape units? 2) How to model the diffusion process and estimate the parameters of the model using incomplete and noisy observations? This document describes my current research progress and future research directions of answering these two important questions.