All of our knowledge about GRBs as radio transients has come via radio follow-up of relativistically- beamed events identified by synoptic survey telescopes at X-ray or gamma-ray wavelengths. However, with the ability to capture off-axis and dust-obscured phenomena, radio surveys offer unique discovery opportunities and strong diagnostics for orphan long-GRB afterglows as well as the coalescence of compact star binaries. The former are expected to be a significantly larger population compared to beamed GRBs, while the latter are the most compelling GW sources expected from aLIGO. I will describe the observational signatures of these transients and argue that observations at radio wavelengths are just as powerful as the optical, if not more, in detecting the EM counterparts of GW sources. The time is ripe for finding these sources due to the availability of sensitive wide-field radio survey facilities and the imminent aLIGO observing runs expected to make ground-breaking discoveries of GW sources within this decade. I will further describe our recently-completed Jansky VLA radio transient program, the Caltech-NRAO Stripe 82 Survey, that has led to the discovery of extragalactic explosion candidates, some of which could be orphan afterglows. I will also explore the potential of the VLA Sky Survey (VLASS) and the surveys planned for the SKA Pathfinders, such as ASKAP and MeerKAT, in the context of finding radio afterglows of orphan GRBs and GW sources.