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.