In the study of neuro-electrophysiological recordings, aperiodic neural activity - activity with no characteristic frequency - has increasingly become a common feature of study. This interest has rapidly extended to clinical work, with many reports investigating aperiodic activity from patients from a broad range of clinical disorders. This work typically seeks to evaluate aperiodic activity as a putative biomarker relating to diagnosis or treatment response, and/or as a potential marker of underlying physiological activity. There is thus far no clear consensus on if and how aperiodic neural activity relates to clinical disorders, nor on the best practices for how to study it in clinical research. To address this, this systematic literature review, following PRISMA guidelines, examines reports of aperiodic activity in electrophysiological recordings with human patients with psychiatric and/or neurological disorders, finding 143 reports across 35 distinct disorders. Reports within and across disorders are summarized to evaluate current findings and examine what can be learned as pertains to the analysis, interpretations, and overall utility of aperiodic neural activity in clinical investigations. Aperiodic activity is commonly reported to relate to clinical diagnoses, with 31 of 35 disorders reporting a significant effect in diagnostic and/or treatment related studies. However, there is variation in the consistency of results across disorders, with the heterogeneity of patient groups, disease etiologies, and treatment status arising as common themes across different disorders. Overall, the current variability of results, potentially confounding covariates, and limitations in current understanding of aperiodic activity suggests further work is needed before aperiodic activity can be established as a potential biomarker and/or marker of underlying pathological physiology. Finally, a series of recommendations are proposed, based on the findings, limitations, and key discussion topics of the current literature to assist with guiding productive future work on the clinical utility of studying aperiodic neural activity.