Histograms are a concise and flexible way to construct summary structures for large data sets. They have attracted a lot of attention in database research due to their utility in many areas, including query optimization, and approximate query answering. They are also a basic tool for data visualization and analysis.In this paper, we present a formal study of dynamic multidimensional histogram structures over continuous data streams. At the heart of our proposal is the use of a dynamic summary data structure (vastly different from a histogram) maintaining a succinct approximation of the data distribution of the underlying continuous stream. On demand, an accurate histogram is derived from this dynamic data structure. We propose algorithms for extracting such an accurate histogram and we analyze their behavior and tradeoffs. The proposed algorithms are able to provide approximate guarantees about the quality of the estimation of the histograms they extract.We complement our analytical results with a thorough experimental evaluation using real data sets.