The pluriclosed flow is a natural geometric evolution equation generalizing Kahler-Ricci flow to the setting of complex, non-Kahler geometry. It was introduced in joint work with G. Tian, aiming at understanding the existence of canonical metrics in Hermitian geometry, and ideally at understanding the topological structure of complex surfaces. In these lectures I will introduce the fundamental geometric and analytic aspects of this flow. In the first lecture I will introduce the equation itself and prove basic analytic results, including a Perelman-type monotonicity formula. In the second lecture I will describe the proofs of various global existence and convergence results. The third lecture will focus on the relationship of pluriclosed flow and generalized Kahler (GK) geometry. In particular, the flow preserves GK geometry and interacts with the basic structures of this geometry in interesting ways. I will describe this connection, prove global existence results in this setting, and describe the implications for understanding the space of all generalized Kahler structures on certain manifolds