How did the popularity of the Greek Prime Minister evolve in 2015? How did the predominant sentiment about him vary during that period? Were there any controversial sub-periods? What other entities were related to him during these periods? To answer these questions, one needs to analyze archived documents and data about the query entities, such as old news articles or social media archives. In particular, user-generated content posted in social networks, like Twitter and Facebook, can be seen as a comprehensive documentation of our society, and thus meaningful analysis methods over such archived data are of immense value for sociologists, historians and other interested parties who want to study the history and evolution of entities and events. To this end, in this paper we propose an entity-centric approach to analyze social media archives and we define measures that allow studying how entities were reflected in social media in different time periods and under different aspects, like popularity, attitude, controversiality, and connectedness with other entities. A case study using a large Twitter archive of four years illustrates the insights that can be gained by such an entity-centric and multi-aspect analysis.