Astronomy, like all sciences, is being revolutionized by the progress in computation and information technology. Central to this is the exponential growth of data volumes, rates, and complexity, now moving from Terascale to Petascale, with the attendant challenges of an effective knowledge extraction and discovery. These demands become much sharper as one moves from a static exploration of fixed data sets, to a dynamical, real-time exploration of massive data streams.We will illustrate some of these challenges and the scientific potential of the synergy of astronomy and computation on an example of a digital, synoptic sky survey now under way at Palomar Observatory. Systematic exploration of the time domain in astronomy spans a broad range of interesting phenomena: from potentially hazardous asteroids to cosmic explosions, and from stellar evolution to extreme relativistic physics. Computational challenges include real-time mining of massive data streams, automated event discovery, classification, dissemination, and follow-up, etc. This is a precursor and a testbed for the future facilities like the Large Synoptic Survey Telescope, which will expand further both the discovery potential and the magnitude of the technical challenges in his arena.