The unique capabilities of Swift that make it ideal for discovery and follow-up of Gamma-Ray bursts also make it the ideal mission for discovery and monitoring of X-ray Transients in the Milky Way and the Large and Small Magellanic Clouds. The Burst Alert Telescope allows for detection of new transient outbursts, the automated follow-up capabilities of Swift allow for rapid observation and localization of the new transient in X-rays and optical/UV bands, and Swift's rapid slewing capabilities allow for low-overhead short observations to be obtained, opening up the possibility of regular, sensitive, long term monitoring of transient outbursts that are not possible with other currently operational X-ray missions. In this paper I describe the methods of discovery of X-ray transients utilizing Swift's BAT and also collaboration with the MAXI telescope. I also detail two examples of X-ray transient science enabled by Swift: Swift discovery and monitoring observations of MAXI J1659-152, a Black Hole candidate Low Mass X-ray Binary in the Galactic Halo, which has the shortest known orbital period of any such system; and Swift monitoring of IGR J00569-7226, an edge on Be/X-ray binary that displayed an outburst in 2013 and 2014, and which monitoring by Swift allowed for detection of dips, eclipses and the determination of the orbital parameters, utilizing a measurement of Doppler shifts in the pulsar period.
