Post-COVID syndrome is increasingly recognized as a new clinical entity in the context of SARS-CoV-2 infection. Symptoms persisting for more than three weeks after the diagnosis of COVID-19 characterize the post-COVID syndrome. Its incidence ranges from 10% to 35%, however, rates as high as 85% have been reported among patients with a history of hospitalization. Currently, there is no consensus on the classification of post-COVID syndrome. We reviewed the published information on post-COVID syndrome, putting emphasis on its pathogenesis. The pathogenesis of post-COVID syndrome is multi-factorial and more than one mechanism may be implicated in several clinical manifestations. Prolonged inflammation has a key role in its pathogenesis and may account for some neurological complications, cognitive dysfunction, and several other symptoms. A multisystem inflammatory syndrome in adults (MIS-A) of all ages has been also described recently, similarly to multisystem inflammatory syndrome in children (MIS-C). The post-infectious inflammatory pathogenetic mechanism of MIS-A is supported by the fact that its diagnosis is established through serology in up to one third of cases. Other pathogenetic mechanisms that are implicated in post-COVID syndrome include immune-mediated vascular dysfunction, thromboembolism, and nervous system dysfunction. Although the current data are indicating that the overwhelming majority of patients with post-COVID syndrome have a good prognosis, registries to actively follow them are needed in order to define the full clinical spectrum and its long-term outcome. A consensus-based classification of post-COVID syndrome is essential to guide clinical, diagnostic, and therapeutic management. Further research is also imperative to elucidate the pathogenesis of post-COVID syndrome.