Inthisreview,weintendtoclarifytheunderlyingideasandtherelationsbetweenvariousmultigridmethodsrangingfromsubsetdecomposition,toprojectedsubspacedecompositionandtruncatedmultigrid.Inaddition,wepresentanovelgloballyconvergentinexactactivesetmethodwhichiscloselyrelatedtotruncatedmultigrid.Thenumericalpropertiesofalgorithmsarecarefullyassessedbymeansofadegenerateproblemandaproblemwithacomplicatedcoincidenceset.
