At present, there exists no consensus in the astronomical community regarding either the bulk composition or the formation mechanism for the interstellar object 1I/2017 U1 ('Oumuamua). With the goal of assessing the merits of the various scenarios that have been suggested to explain 'Oumuamua's appearance and observed properties, we report a number of new analyses and provide an up-to-date review of the current hypotheses. We consider the interpretations that can reconcile 'Oumuamua's observed non-Keplerian trajectory with the non-detection of traditional cometary volatiles. We examine the ability of these proposed formation pathways to populate the galaxy with sufficient interstellar objects such that the detection of 'Oumuamua by Pan-STARRS would be statistically-favored. We consider two exotic ices, hydrogen and nitrogen, showing that the frigid temperature requirement for the former and the necessary formation efficiency of the latter pose serious difficulties for these interpretations. Via order-of-magnitude arguments and hydrodynamical cratering simulations, we show that impacts on extrasolar Kuiper Belt analogues are not expected to generate N2 ice fragments as large as 'Oumuamua. In addition, we discuss observational tests to confirm the presence of these ices in future interstellar objects. Next, we examine the explanations that attribute 'Oumuamua's properties to other compositions: ultra-porous dust aggregates and thin membranes powered by solar radiation pressure, among others. While none of these hypotheses are perfectly satisfactory, we make predictions that will be testable by the Vera Rubin Observatory to resolve the tension introduced by 'Oumuamua.