Consider a video surveillance application that monitors some location. The application knows a set of activity models (that are either normal or abnormal or both), but in addition, the application wants to find video segments that are unexplained by any of the known activity models - these unexplained video segments may correspond to activities for which no previous activity model existed. In this paper, we formally define what it means for a given video segment to be unexplained (totally or partially) w.r.t. a given set of activity models and a probability threshold. We develop two algorithms - FindTUA and FindPUA - to identify Totally and Partially Unexplained Activities respectively, and show that both algorithms use important pruning methods. We report on experiments with a prototype implementation showing that the algorithms both run efficiently and are accurate.