This thesis provides an empirically driven and theoretically informed examination of temporal, aspectual and modal (TAM) expression in Anindilyakwa, an underdescribed and underdocumented Gunwinyguan language of the Groote Eylandt archipelago, north-east Arnhem Land, Australia. The goals of the thesis are both descriptive and theoretical. The first is to provide a detailed description of some of the core grammatical properties of Anindilyakwa, particularly related to the verbal complex. This descriptive goal is linked to, and builds the infrastructure for, the second goal of the thesis: to provide a theoretically-informed examination of temporal, aspectual and modal expression and interaction in Anindilyakwa, thus contributing towards (and building upon) research in the area of TAM semantics and pragmatics (and their interfaces with morpho-syntax). The original contribution of this thesis lies in the cross-section between theoretically-informed morpho-syntactic, semantic and pragmatic approaches to TAM expression in natural languages, and the exploration and examination of this domain in a fieldwork and language documentation setting: how do underdescribed languages inform our understanding of this domain, and how should we approach the documentation of these concepts in the field? Anindilyakwa is a particularly interesting language to examine in this regard, given the polysynthetic nature and complex morphological make-up and combinatorics of the verb. Inflectionally, TAM expression is realised through the combination of (at least) two discontinuous morphological slots of the verb structure. In addition to the complex morphological combinatorics of the verbal structure, this inflectional system displays widespread aspectuo-temporal underspecification, coupled with a widespread lack of contrastiveness in many of the paradigmatic forms (i.e. syncretism). Thus, unpacking and understanding these inflectional verbal properties, with respect to TAM expression, is where the core of this thesis lies. This comprehensive semantic and morpho-syntactic investigation into the TAM system of Anindilyakwa contributes not only to the description of this underdocumented language, but it also bolsters the representation of understudied (particularly non-European) languages that have received detailed TAM study, ensuring that future cross-linguistic typological work on TAM has access to richer data in a wider sample of the world's languages.