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Astrophysical transients have been observed for millennia and have shaped our most basic assumptions about the Universe. In the last century, systematic searches have grown from detecting handfuls of transients per year to over 7000 in 2018 alone. As these searches have matured, we have discovered both large samples of "normal" classes and new, rare classes. Recently, a transient was the first object observed in both gravitational waves and light. Ground-based observatories, including LSST, will discover thousands of transients in the optical, but these facilities will not provide the high-fidelity near-infrared (NIR) photometry and high-resolution imaging of a space-based observatory. WFIRST can fill this gap. With its survey designed to measure the expansion history of the Universe with Type Ia supernovae, WFIRST will also discover and monitor thousands of other transients in the NIR, revealing the physics for these high-energy events. Small-scale GO programs, either as a supplement to the planned survey or as specific target-of-opportunity observations, would significantly expand the scope of transient science that can be studied with WFIRST.