The goal of this roadmap paper is to summarize the state-of-the-art and identify research challenges when developing, deploying and managing self-adaptive software systems. Instead of dealing with a wide range of topics associated with the field, we focus on four essential topics of self-adaptation: design space for self-adaptive solutions, software engineering processes for self-adaptive systems, from centralized to decentralized control, and practical run-time verification & validation for self-adaptive systems. For each topic, we present an overview, suggest future directions, and focus on selected challenges. This paper complements and extends a previous roadmap on software engineering for self-adaptive systems published in 2009 covering a different set of topics, and reflecting in part on the previous paper. This roadmap is one of the many results of the Dagstuhl Seminar 10431 on Software Engineering for Self-Adaptive Systems, which took place in October 2010.