Algebraic Multigrid (AMG) has been shown to be a very effective solver for standard finite-difference and finite-element discretizations of a wide range of second-order elliptic PDEs. This talk covers some of the issues related to the use of AMG on discretizations using higher-order finite elements.  These include: problems encountered when no special handling is used; variations of the AMG algorithm better suited for such problems; the effect of the choices of basis functions; and measures of accuracy versus work for various orders of approximation. Numerical results are reported.