We study the impact of algorithmic trading in the foreign exchange market using a long time series of high-frequency data that specifically identifies computer-generated trading activity. Using both a reduced-form and a structural estimation, we find clear evidence that algorithmic trading causes an improvement in two measures of price efficiency in this market: the frequency of triangular arbitrage opportunities and the autocorrelation of high-frequency returns. Relating our results to the recent theoretical literature on the subject, we show that the reduction in arbitrage opportunities is associated primarily with computers taking liquidity, while the reduction in the autocorrelation of returns owes more to the algorithmic provision of liquidity. We also find evidence that algorithmic traders do not trade with each other as much as a random matching model would predict, which we view as consistent with their trading strategies being highly correlated. However, the analysis shows that this high degree of correlation does not appear to cause a degradation in market quality.