M onetary economists long have thought that government injections of money into a macroeconomy have a certain neutral effect. The main idea is that changes in the money stock eventually change nominal prices and nominal wages, ultimately leaving important real variables, like real output, real consumption expenditures, real wages, and real interest rates, unaffected. Since economic decision making is based on real factors, the long-run effect of injecting money into the macroeconomy is often described as neutral—in the end, real variables do not change and so economic decision making is also unchanged. How long such a process takes, and what might happen in the meantime, are hotly debated questions. But relatively few economists debate the merits of long-run neutrality. Indeed, long-run neutrality is instead taken as a given, almost an axiom, a logical consequence of suppositions made in economic theory. Curiously, during most of the postwar period the empirical evidence on long-run monetary neutrality has been in a state of flux. No doubt this is in part because it is difficult to look at the data generated by the world’s economies and come to any firm conclusion about whether monetary injections had important real effects, in the short run or in the long run. In addition, many of the empirical tests that were devised ran into important criticisms that seemed to invalidate their conclusions. These criticisms were based, at least in part, on questionable handling or interpretation of the time-series properties of the data. In recent years, however, economists have devised new tests of long-run monetary neutrality, as well as related neutralitytype propositions. A fair amount of literature has been written on the subject, and the purpose of this paper is to review this literature.1 The next section provides more detail concerning the background behind the current empirical tests of neutrality propositions. In the following sections, some of the recent research using the newer set of tests is reviewed, and a few related papers are discussed along with the results authors have found using somewhat different methodologies. The final section offers some comments about directions for future research.