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Nowadays, object-oriented (OO) languages are widely used in the development of many different kinds of applications. However, testing those applications is still very expensive and time-consuming for the software community. The automation of this task would therefore be highly desirable. Although automatic testing of procedural software has been studied in depth for many years, comparatively little work has been done about OO software. Different techniques exist. However, the most promising one is probably to model the task as a search problem. This paper explains why automatic testing of OO software is more difficult than procedural software. These difficulties provide strong challenges to the natural computation and software engineering communities. A brief review of the literature of the subject follows. The issues of the current state-of-art of the field are then outlined. Finally, some open research problems are discussed.