Verbs are often understood in terms of the events they denote and the events' participants. These participants are typically classified as core or peripheral participants, which correspond to arguments and adjuncts, respectively. Consider Cathy won the contest last year. Cathy and the contest are core participants and arguments whereas last year is a peripheral participant and an adjunct, respectively. Despite an intuitive distinction between arguments and adjuncts, the exact nature of this distinction has been difficult to characterize. This thesis contributes to our understanding of argument structure through two different approaches. We first conducted a cross-linguistic investigation of instrument phrases, which are notoriously difficult to characterize as arguments or adjuncts. This study revealed three factors that contribute to the controversial status of instruments: the semantics/syntax misalignment, the allow/require distinction, and the body-part/external instruments distinction. Next we conducted an investigation of verbs and their participants in atypical populations. This study provided evidence that individuals with high functioning autism and individuals with loss of diagnosis may present with subtle argument structure impairments; proposed novel measures of language assessment that capture individual differences otherwise missed; and advocated for an alternative method of analysis that accounts for within-group variability. Together, the two studies contribute to our understanding of some of the factors involved in distinguishing between arguments and adjuncts and highlight how argument structure concepts can be applied to better serve individuals with high functioning autism and with loss of diagnosis.