Human African trypanosomiasis (HAT) or sleeping sickness is a neglected tropical disease with a progressive central nervous system (CNS) involvement and marked sleep and circadian rhythm abnormalities. Even though this is a prominent feature of HAT, the connection between parasite neuroinvasion, neuroinflammation, circadian dysfunction, and neurological impairment is not fully understood. This narrative review aims to summarize the most up-to-date knowledge about sleep and circadian disturbance in HAT and proposes an integrated approach for the Trypanosome-Associated Sleep Disorder (TASD). The relevant literature was identified by searching major biomedical databases for HAT, sleep disorders, circadian rhythms, neuroinflammation, and CNS invasion. The review covers the steps by which the CNS becomes invaded, how the barriers are disrupted, how the CNS becomes activated by inflammatory responses, and how the hypothalamic and circadian regulatory networks are disrupted. The evidence suggests that excessive daytime sleepiness, fragmented nocturnal sleep, circadian misalignment, and neuropsychiatric manifestations are related to the activation of inflammatory cytokines, altered neurotransmitter signaling, activation of the kynurenine pathway, dysregulation of clock genes, and disruption of the suprachiasmatic nucleus. We also discuss TASD as a syndrome-like phenotype of CNS involvement and propose a three-stage model of sleep-wake dysfunction in HAT. The review unites these integral mechanisms in a single mechanistic framework to offer a unified understanding of the sleep pathology associated with HAT. There are still important gaps in our knowledge of biomarkers, disease staging, and irreversible neuronal damage, which indicate priorities for future research and better clinical management.