Introspection is considered a key method for exploring the workings of the psyche because psychical phenomena are accessible only by the individual him or herself. But this epistemological concept, despite its importance, remained unclear and contentious. Its scientificity is often questioned, but still introspective findings from psychophysics are widely accepted as the ultimate proof of the quantifiability of psychical phenomena. Not everything going on in individuals' minds is considered introspection, but clear criteria that qualify explorations as introspective are still missing. This research applies the Transdisciplinary Philosophy-of-Science Paradigm for Research on Individuals (TPS-Paradigm) to metatheoretically define the peculiarities of psychical phenomena of which various kinds are differentiated and to derive therefrom basic methodological principles and criteria applicable to any investigation. Building on these foundations, the TPS-Paradigm introduces the concepts of introquestion versus extroquestion and reveals that introspection cannot be clearly differentiated from extrospection and that psychophysical experiments and some first-person perspective methods are not introspective as often assumed. The chapter explores the challenges that arise from the fact that psychical phenomena can be explored only indirectly through individuals' behavioural and semiotic externalisations and scrutinises what, when, where and how to externalise in introquestive explorations. The basic principles and criteria elaborated also allow for determining which kind of psychical phenomenon can be explored by using which kind of method for establishing an appropriate phenomenon–methodology match.