We show that in the world of Black and Scholes (1973) lookback options where the underlying price is monitored discretely instead of continuously can be priced in semi-closed form. We derive pricing formulas for a variety of full and partial lookback options, where monitoring takes place at not necessarily equally-spaced points in time. Analysis of the results shows that monitoring the underlying price discretely instead of continuously may have a significant effect on the prices of lookback options but does not introduce new hedging problems.