Agile methods are widely adopted by the industry. Their promise is that the development primarily targets at delivering value to end users in each increment, in contrast to following a pre-made plan. At the same time, the expectation is that as the developers get feedback from the end users early on, also quality of the resulting systems meets the expectation. In this paper, we study the amount of empirical evidence on the benefits of agile methods that has been scientifically confirmed. The goal is to understand perceived benefits and downsides of agile development, as well as the a time line of these studies. As the research method, we have performed a systematic literature review, following the established practices. The results indicate that we have far less empirical results than one would expect, based on the popularity of agile software development.