In recent years, substantial effort has been focused on developing methods capable of solving the large linear systems that arise from the discretization of partial differential equations, especially on unstructured grids. Through this work, multigrid methods have emerged as a mature multiscale technology for solving many such linear systems. In this talk, we present a recent extension to the algebraic multigrid methodology that adaptively constructs the multigrid hierarchy based on the response of the evolving multigrid method itself. Such an approach allows effective solution of a wider class of problems. We also discuss the multiscale nature of the coarse-grid operators used in this, and other, variational multigrid approaches and their relationship to upscaling.