Hypoelliptic operators live in an interesting corner of the world of PDE, in which geometry plays a crucial role. Lie groups are a natural setting for the study of these operators, but even for simple examples such as the Heisenberg group, many questions remain open. I will give an overview and examples of what these objects are and how they behave, and discuss some recent results involving estimates for hypoelliptic heat kernels on H-type groups, a class of Lie groups which generalize some of the properties of the Heisenberg group. All are welcome to attend.