Random sampling is an appealing approach to build synopses of large data sets because random samples can be used for a broad spectrum of analytical tasks. Current research mainly considers the database static; in this setting, a sample created once remains valid for its entire lifetime. In many applications, however, such a static view is infeasible because it does not take into account the dynamic nature of the underlying data. In this talk, I will briefly summarize recent research on the problem of maintaining a random sample of an evolving dataset. As an example for the challenges of sample maintenance and the techniques required to solve them, I will discuss the problem of maintaining a random sample from a sliding window a data stream defined over a recent time interval. In this setting, the main challenge is to guarantee an upper bound on the space consumption of the sample while using the allotted space efficiently at the same time. The difficulty arises from the fact that the number of items in the window is unknown in advance and may vary significantly over time, so that the sampling fraction has to be adjusted dynamically. Within the talk, I will outline a novel sampling scheme called bounded priority sampling (BPS), which requires only bounded space and quickly adapts to changing data