An automated, rapid classification of transient events detected in the modern synoptic sky surveys is essential for their scientific utility and effective follow-up using scarce resources. This presents some unusual challenges: the data are sparse, heterogeneous and incomplete; evolving in time; and most of the relevant information comes not from the data stream itself, but from a variety of archival data and contextual information (spatial, temporal, and multi-wavelength). We are exploring a variety of novel techniques, mostly Bayesian, to respond to these challenges, using the ongoing CRTS sky survey as a testbed. The current surveys are already overwhelming our ability to effectively follow all of the potentially interesting events, and these challenges will grow by orders of magnitude over the next decade as the more ambitious sky surveys get under way. While we focus on an application in a specific domain (astrophysics), these challenges are more broadly relevant for event or anomaly detection and knowledge discovery in massive data streams.