The functioning of the central nervous system (CNS) is the result of the constant integration of bidirectional messages between the brain and peripheral organs, together with their connections with the environment. Despite the anatomical separation, gut microbiota, i.e., the microorganisms colonising the gastrointestinal tract, is highly related to the CNS through the so-called “gut–brain axis”. The aim of this paper was to review and comment on the current literature on the role of the intestinal microbiota and the gut–brain axis in some common neuropsychiatric conditions. The recent literature indicates that the gut microbiota may affect brain functions through endocrine and metabolic pathways, antibody production and the enteric network while supporting its possible role in the onset and maintenance of several neuropsychiatric disorders, neurodevelopment and neurodegenerative disorders. Alterations in the gut microbiota composition were observed in mood disorders and autism spectrum disorders and, apparently to a lesser extent, even in obsessive-compulsive disorder (OCD) and related conditions, as well as in schizophrenia. Therefore, gut microbiota might represent an interesting field of research for a better understanding of the pathophysiology of common neuropsychiatric disorders and possibly as a target for the development of innovative treatments that some authors have already labelled “psychobiotics”.