Autism spectrum disorder (ASD) is a neurodevelopmental disorder that affects several areas of mental development. The onset of ASD occurs in the first few years of life, usually before the age of 3 years. Proper nutrition is important to ensure that an individual’s nutrient and energy requirements are met, and it can also have a moderating effect on the progression of the disorder. A systematic database search was conducted as a narrative review to determine whether nutrition and specific diets can potentially alter gastrointestinal symptoms and neurobehavioral disorders. Databases such as Science Direct, PubMed, Scopus, Web of Science (WoS), and Google Scholar were searched to find studies published between 2000 and September 2023 on the relationship between ASD, dietary approaches, and the role of dietary components. The review may indicate that despite extensive research into dietary interventions, there is a general lack of conclusive scientific data about the effect of therapeutic diets on ASD; therefore, no definitive recommendation can be made for any specific nutritional therapy as a standard treatment for ASD. An individualized dietary approach and the dietician’s role in the therapeutic team are very important elements of every therapy. Parents and caregivers should work with nutrition specialists, such as registered dietitians or healthcare providers, to design meal plans for autistic individuals, especially those who would like to implement an elimination diet.