Human social dynamics are often ignored in models of environment systems, and likewise environment dynamics are often ignored in models of human social systems. Interest in models that acknowledge the two-way coupling between human and environmental systems has grown steadily over the past few decades, and has accelerated especially in recent years in the face of growing environmental catastrophes of our own making. Here we will demonstrate how mathematical models – even relatively simple ones – can play an important role in the study of coupled human-environment systems (HES). We will discuss what happens to dynamics when human and environmental systems are coupled; give an overview of some mathematical HES models that incorporate natural dynamics, harvesting, social learning social norms, conservation values and economic factors; and describe some of their predictions. Study systems include forest conservationism, forest pests, and coral reef conservationism. This presentation is based on joint work of the Anand and Bauch research groups.