ABSTRACT. This paper reviews a variety of criteria which have been proposed for legislative and congressional redistricting in the US and discusses the political and legal factors which have shaped 1980s redistricting. Particular attention is paid to the conflicts of interest between incumbents (seeking re-election), party organizations (seeking aggregate partisan advantage), minority interests (seeking proportional minority representation or at least enhanced minority influence), liberal reformers (seeking to take the 'politics' out of the redistricting process), and courts (seeking largely to implement 'one person, one vote' guidelines by minimizing deviation from population equality across districts but also concerned with avoiding dilutions of minority voting strength). It calls attention to three phenomena which have made redistricting in the 1980s different from that of earlier decades: (1) the striking role of the Justice Department in using the pre-clearance provision of the Voting Rights Act to assure greater minority voting strength and to eliminate discriminatory use of multi-member districting schemes; (2) the increased political and legal sophistication of minority groups; and (3) the role of the computer in making available a plethora of districting plans, all of which satisfy court equipopulation guidelines but which differ dramatically from each other in their substantive implications for the representation of political, racial, linguistic, and socio-economic groupings, and in their implications for the likely political fate of incumbent politicians and their potential challengers.