Background: Since the first discussions of new challenges posed by aspect-oriented programming (AOP) to software testing, the real difficulties of testing aspect-oriented (AO) programs have not been properly analysed. Firstly, despite the customisation of traditional testing techniques to the AOP context, the literature lacks discussions on how hard it is to apply them to (even ordinary) AO programs based on practical experience. Secondly, and equally important, due to the cautious AOP adoption focused on concern refactoring, test reuse is another relevant issue that has been overlooked so far. This paper deals with these two issues. It discusses the difficulties of testing AO programs from three perspectives: (i) structural-based testing, (ii) fault-based testing and (iii) test set reuse across paradigms. Methods: Perspectives (i) and (ii) are addressed by means of a retrospective of research done by the authors' group. We analyse the impact of using AOP mechanisms on the testability of programs in terms of the underlying test models, the derived test requirements and the coverage of such requirements. The discussion is based on our experience on developing and applying testing approaches and tools to AspectJ programs at both unit and integration levels. Perspective (iii), on the other hand, consists of recent exploratory studies that analyse the effort to adapt test sets for refactored systems and the quality of such test sets in terms of structural coverage. Results: Building test models for AO programs imposes higher complexity when compared to the OO paradigm. Besides this, adapting test suites for OO programs to AO equivalent programs tends to require less effort than doing the other way around, and resulting suites achieve similar quality levels for small-sized aplications. Conclusions: The conclusion is that building test models for AO programs, as well as deriving and covering paradigm-specific test requirements, is not straightforward as it has been for procedural and object-oriented (OO) programs at some extent. Once you have test suites in conformance with programs implemented in both paradigms, the quality of such suited in termos of code coverage may vary depending on the size and characteristics of the applications under testing.