We survey recent work on competition in markets in which consumers have costs of switching between competing firms' products. In a market with switching costs (or ''brand loyalty''), a firm's current market share is an important determinant of its future profitability. We examine how the firm's choice between setting a low price to capture market share, and setting a high price to harvest profits by exploiting its current locked-in customers, is affected by the threat of new entry, interest rates, exchange rate expectations, the state of the business cycle, etc. We also discuss the causes of switching costs; explain introductory offers and price wars; examine industry profits; and analyse firms' product choices. Moreover, we argue that switching costs between suppliers help explain both the existance of multi-product firms and the nature of competition between such firms.