In the coming decade LSST's combination of all-sky coverage, consistent long-term monitoring and flexible criteria for event identification will revolutionize studies of a wide variety of astrophysical phenomena. Time-domain science with LSST encompasses objects both familiar and exotic, from classical variables within our Galaxy to explosive cosmological events. Increased sample sizes of known-but-rare observational phenomena will quantify their distributions for the first time, thus challenging existing theories. Perhaps most excitingly, LSST will provide the opportunity to sample previously untouched regions of parameter space. LSST will generate ‘alerts’ within 60 seconds of detecting a new transient, permitting the community to follow up unusual events in greater detail. However, follow-up will remain a challenge as the volume of transients will easily saturate available spectroscopic resources. Characterization of events and access to appropriate ancillary data (e.g. from prior observations, either in the optical or in other passbands) will be of the utmost importance in prioritizing follow-up observations. The incredible scientific opportunities and unique challenges afforded by LSST demand organization, forethought and creativity from the astronomical community. To learn more about the telescope specifics and survey design, as well as obtaining a overview of the variety of the scientific investigations that LSST will enable, readers are encouraged to look at the LSST Science Book: http://www.lsst.org/lsst/scibook. Organizational details of the LSST science collaborations and management may be found at http://www.lsstcorp.org.