Software ecosystems are collections of interacting and communicating software projects developed by the same developer community. Dealing with the complex interaction and dynamics of these ecosystems is an important problem that raises additional challenges compared to the maintenance of individual software systems. In particular, the social aspect becomes crucial, requiring to understand evolving ecosystems as dynamic socio-technical networks. Based on software repository mining research advances, in this lecture I explore the state of the art in the empirical analysis of software ecosystems, with a focus on the evolutionary aspect. I present some of the challenges that need to be overcome during the extraction and cleaning of data obtained from different data sources (such as version control repositories, bug trackers, and mailing lists). I draw an analogy between software ecosystems and natural ecosystems, and illustrate through previously reported empirical case studies how ecological diversity metrics and econometric inequality metrics can be used to increase understanding of evolving software ecosystems from dual viewpoints. It should be noted that this article has been conceived as a work of reference. It does not provide any novel research results by itself, but rather introduces the important concepts and challenges in the field. It also provides many pointers for further reading for those researchers that wish to start working in this important research domain.