We review the derivation of moment equations which include the effects of space charge and dispersion in bends first presented in ref. [1]. These equations generalize the familiar envelope equations to include the dispersive effects of bends. We review the application of these equations to the calculation of the change in emittance resulting from a sharp transition from a straight section to a bend section, using an energy conservation constraint. Comparisons of detailed 2D and 3D simulations of intense beams in rings using the WARP code (refs. [2,3]) are made with results obtained from the moment equations. We also compare the analysis carried out in ref. [1], to more recent analyses, refs. [4,5]. We further examine self-consistent distributions of beams in bends and discuss the relevance of these distributions to the moment equation formulation. ©1998 American Institute of Physics.