The Swift/Burst Alert Telescope (BAT) hard X-ray transient monitor provides near real-time coverage of the X-ray sky in the energy range 15-50 keV. The BAT observes 88% of the sky each day with a detection sensitivity of 5.3 mCrab for a full-day observation and a time resolution as fine as 64s. The three main purposes of the monitor are (1) the discovery of new transient X-ray sources, (2) the detection of outbursts or other changes in the flux of known X-ray sources, and (3) the generation of light curves of more than 900 sources spanning over eight years. The primary interface for the BAT transient monitor is a public Web site. Between 2005 February 12 and 2013 April 30, 245 sources have been detected in the monitor, 146 of them persistent and 99 detected only in outburst. Among these sources, 17 were previously unknown and were discovered in the transient monitor. In this paper, we discuss the methodology and the data processing and filtering for the BAT transient monitor and review its sensitivity and exposure. We provide a summary of the source detections and classify them according to the variability of their light curves. Finally, we review all new BAT monitor discoveries. For the new sources that are previously unpublished, we present basic data analysis and interpretations.