Many COVID-19 patients report persistent symptoms, including cognitive disturbances. We performed a scoping review on this topic, focusing primarily on cognitive manifestations. Abstracts and full texts of studies published on PubMed (until May 2023) addressing cognitive involvement persisting after SARS-CoV-2 infection were reviewed, focusing on terms used to name the cognitive syndrome, reported symptoms, their onset time and duration, and testing batteries employed. Reported psychiatric symptoms, their assessment tools, and more general manifestations were also extracted. Among the 947 records identified, 180 studies were included. Only one third of them used a label to define the syndrome. A minority of studies included patients according to stringent temporal criteria of syndrome onset (34%), whereas more studies reported a minimum required symptom duration (77%). The most frequently reported cognitive symptoms were memory and attentional-executive disturbances, and among psychiatric complaints, the most frequent were anxiety symptoms, depression, and sleep disturbances. Most studies reported fatigue among general symptoms. Thirty-six studies employed cognitive measures: screening tests alone (n = 19), full neuropsychological batteries (n = 25), or both (n = 29); 30 studies performed psychiatric testing. Cognitive deficits were demonstrated in 39% of subjects, the most frequently affected domains being attention/executive functions (90%) and memory (67%). Currently, no agreement exists on a label for post-COVID-19 cognitive syndrome. The time of symptom onset after acute infection and symptom duration are still discussed. Memory and attention-executive complaints and deficits, together with fatigue, anxiety, and depression symptoms, are consistently reported, but the objective evaluation of these symptoms is not standardized.