This review describes interactions between monetary and fiscal policies that affect equilibrium price levels and interest rates by critically surveying theories about ( a) optimal anticipated inflation, ( b) optimal unanticipated inflation, and ( c) conditions that secure a nominal anchor in the sense of a unique price level path. We contrast incomplete theories whose inputs are budget-feasible sequences of government-issued bonds and money with complete theories whose inputs are bond/money strategies described as sequences of functions that map time t histories into time t government actions. We cite historical episodes that confirm the theoretical insight that lines of authority between a Treasury and a central bank can be ambiguous, obscure, and fragile. Expected final online publication date for the Annual Review of Economics, Volume 12 is August 3, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.