Atherosclerosis is an important component of cardiovascular disease and usually occurs in medium-sized and large arteries. There are many different types of atherosclerotic plaque, each with its own distinctive composition and characteristics. For example, late-stage plaques tend to be highly inflamed and contain interior regions of necrosis. On the other hand, intimal thickenings are more homogeneous and consist mainly of smooth muscle cells and their products. In this talk I will present some simple PDE and free boundary models to describe the growth, and change in composition of, different types of atherosclerotic plaque. These models aim to give some physical insight into a highly complex disease.