Over the past two decades, Algebraic Multigrid (AMG) has become a prominent tool for the rapid solution of unstructured-grid problems. For nearly 20 years after its inception, AMG was largely ignored, due to the overhead and setup costs necessary to create the components of the algorithm. So long as geometrically structured grids were the norm, this condition persisted. In recent years, however, as unstructured grids became more common and as the problem sizes grew to demand large-scale massively parallel computers, AMG has emerged as a widely used methodology. In this talk we describe the basic components and theory of AMG. Here, the focus is on the underlying philosophy of the method. We then concentrate on the more recent advances in AMG, and in particular on the development of the Bootstrap AMG framework.