This paper examines two ways in which competition works in modern capitalist economies to improve productivity. The first is through incentives: encouraging improvements in technology, organisation and effort on the part of existing establishments and firms. The second is through selection: replacing less-productive with more productive establishments and firms, whether smoothly via the transfer of market shares from less to more productive firms, or roughly through the exit of some firms and the entry of others. We report evidence from the UK suggesting that selection is responsible for a large proportion of aggregate productivity growth in manufacturing, and that much of this is due in turn to selection between plants belonging to multi-plant firms. We also investigate whether the nature of the selection process varies across the business cycle and report evidence suggesting that it is less effective in booms and recessions. Finally, although in principle productivity catch-up by low-income countries ought to be easier than innovation at the frontier, in the absence of a well functioning competitive infrastructure (a predicament that characterises many poor countries), selection may be associated with much more turbulence and a lower rate of productivity growth than in relatively prosperous societies. We report results of a survey of firms in transition economies suggesting that, particularly in the former Soviet states (excluding the Baltic states), poor output and productivity performance has not been due to an unwillingness on the part of firms to change and adapt. On the contrary, there has been a great deal of restructuring, much new entry and large reallocations of output between firms; but such activity has been much more weakly associated with improved performance than we would expect in established market economies.