What is a heat kernel? Why should you care? When can we estimate heat kernels and what do they look like? In this talk, we will attempt to answer these and related questions. We will begin by looking at the heat equation in $\mathbb{R}^n$ from both analytic and probabilistic perspectives and then consider how to estimate heat kernels in more general settings, such as on Riemannian manifolds. Very little background is assumed, and there will be pictures!