We propose frameworks and algorithms for identifying communities in social networks that change over time. Communities are intuitively characterized as “unusually densely knit” subsets of a social network. This notion becomes more problematic if the social interactions change over time. Aggregating social networks over time can radically misrepresent the existing and changing community structure. Instead, we propose an optimization-based approach for modeling dynamic community structure. We prove that finding the most explanatory community structure is NP-hard and APX-hard, and propose algorithms based on dynamic programming, exhaustive search, maximum matching, and greedy heuristics. We demonstrate empirically that the heuristics trace developments of community structure accurately for several synthetic and real-world examples.