Computer software fails because of the presence of intellectual faults, ranging from simple coding faults to fundamental design faults. In principle, such faults can be permanently removed when they are detected by failure of the software. Then the software will exhibit reliability growth. The problem considered here is the one of forecasting this growth: it includes the estimation of the current reliability of the program from the previous failure data. We begin with a brief description of the software failure process: a non-stationary stochastic process. Several of the best-known software reliability growth models are described, and examples given of their performance on real software failure data. They shown marked disagreement and thus reveal a need for methods of comparing and evaluating software reliability forecasts. Several simple techniques for conducting this evaluation are described and illustrated using several different models on real data sets. Finally, it is shown how in certain circumstances it is possible to improve the predictive accuracy of software reliability models by a re-calibration technique.