Exploration of the time domain - variable and transient objects and phenomena - is rapidly becoming a vibrant research frontier, touching on essentially every field of astronomy and astrophysics, from the Solar system to cosmology. Time domain astronomy is being enabled by the advent of the new generation of synoptic sky surveys that cover large areas on the sky repeatedly, and generating massive data streams. Their scientific exploration poses many challenges, driven mainly by the need for a real-time discovery, classification, and follow-up of the interesting events. Here we describe the Catalina Real-Time Transient Survey (CRTS), that discovers and publishes transient events at optical wavelengths in real time, thus benefiting the entire community. We describe some of the scientific results to date, and then focus on the challenges of the automated classification and prioritization of transient events. CRTS represents a scientific and a technological testbed and precursor for the larger surveys in the future, including the Large Synoptic Survey Telescope (LSST) and the Square Kilometer Array (SKA).