This paper gives a detailed description of how adaptivity is realized in e-learning systems, with a focus on adaptivity of courseware. The review aims to answer three basic questions on adaptive courseware: what has been adapted, how and why. Researchers have tried to adapt according to these different elements: student knowledge, behaviour, interests, preferences, learning style, cognitive style, goals, courseware presentation, navigation, annotation, sequencing and knowledge testing. An historical background of adaptivity is described: from word definition, through adaptive instructions and adaptive systems, all the way to adaptive courseware. The biggest challenge was to find the most prominent representatives of adaptive systems in courseware generation that were selected after an exhaustive search through relevant scientific paper databases. Each prevailing system is briefly described and the student features, to which the system adapts, are highlighted, together with the level of adaptation. This paper aims to provide important information to researchers, educators and software developers of computer-based educational software ranging from e-learning systems in general to intelligent tutoring systems in particular. Such an analysis has not been done so far, especially in a way that adaptive systems are described uniformly. Finally, a comparative analysis of those systems and conclusions and demands about the ultimate adaptive system is given. This paper can be used as a guide for making decisions about what to adapt, how and why, while designing an adaptive e-learning system.