Τhe importance of the gut microbiome and its functions has only recently been recognized and researched in greater depth. The establishment of the human gut microbiome begins in utero, forming its adult-like phenotype in the first 2–3 years of life. Several factors affect and alter the gut microbiome composition and its metabolic functions, such as early onset of breastfeeding, mode of delivery, antibiotic administration, or exposure to chemical substances, among others. Existing data support the important connection between health status and gut microbiome homeostasis. In cases when this balance is disturbed, several disorders may arise, such as inflammatory reactions that lead to atopy, eczema, or allergic asthma. The so-called gut-brain axis refers to the complex biochemical pathways between the central nervous system and the gastrointestinal system. One of the most fascinating areas of ongoing research is the broad spectrum of neurodevelopmental disorders (NDDs) and how gut health may be associated with such disorders. The prevalence of NDDs, such as autism spectrum disorder or attention deficit hyperactivity disorder, has increased over recent years. Whether gut microbiota homeostasis plays a role in these disorders is not yet fully understood. The aim of this narrative review is to provide an account of current knowledge on how gut health is linked with these disorders. We performed a literature review in order to identify and synthesize available data that highlights the potential association between NDDs and a balanced gut microbiome in terms of composition and proper function. The connection between the gut microbiome and NDDs offers promising new opportunities for future research.