Sciences studying the deep past, including cosmology, reconstruct past phenomena from often meager remnants available in the present. This leads to prolonged periods of indecisiveness about discrepant theoretical explanations and models. The chapter argues that the notion of the so-called underdetermination of competing theories by evidence captures the epistemic situation that characterizes modern cosmology. The logical notion of underdetermination of competing theories predicated on total possible evidence is not so interesting in understanding and tracking details of the actual historical episodes. An historical notion of underdetermination more realistically assumes only partially equivalent evidential bases of competing theories. Protracted periods of underdetermination also question idealized notions of observational facts as opposed to speculative theories, as pointed out by Bondi in the 1950s. Prematurely establishing certain observations as immutable facts, which, in turn, eliminates various theoretical accounts, impedes the field that operates at the observational limit. The chapter argues that a qualified notion of these concepts is needed to approach historical analysis of cosmology properly.