More than 40% of individuals infected by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have experienced persistent or relapsing multi-systemic symptoms months after the onset of coronavirus disease 2019 (COVID-19). This post-COVID-19 condition (PCC) has debilitating effects on the daily life of patients and encompasses a broad spectrum of neurological and neuropsychiatric symptoms including olfactory and gustative impairment, difficulty with concentration and short-term memory, sleep disorders and depression. Animal models have been instrumental to understand acute COVID-19 and validate prophylactic and therapeutic interventions. Similarly, studies post-viral clearance in hamsters, mice and nonhuman primates inoculated with SARS-CoV-2 have been useful to unveil some of the aspects of PCC. Transcriptomic alterations in the central nervous system, persistent activation of immune cells and impaired hippocampal neurogenesis seem to have a critical role in the neurological manifestations observed in animal models infected with SARS-CoV-2. Interestingly, the proinflammatory transcriptomic profile observed in the central nervous system of SARS-CoV-2-inoculated mice partially overlaps with the pathological changes that affect microglia in humans during Alzheimer's disease and aging, suggesting shared mechanisms between these conditions. None of the currently available animal models fully replicates PCC in humans; therefore, multiple models, together with the fine-tuning of experimental conditions, will probably be needed to understand the mechanisms of PCC neurological symptoms. Moreover, given that the intrinsic characteristics of the new variants of concern and the immunological status of individuals might influence PCC manifestations, more studies are needed to explore the role of these factors and their combinations in PCC, adding further complexity to the design of experimental models.