Autism spectrum disorder (ASD) is a complex neurodevelopmental condition impacting behavior, communication, and social interaction. The term “spectrum” highlights the variability in symptoms and severity, ranging from mild to severe. While ASD typically manifests within the first two years of life, it can remain undiagnosed until adolescence. The exact causes of ASD are still unclear, though genetic research continues to provide valuable insights. Early detection and intervention are essential for better outcomes, enabling timely support and therapy. Leveraging big data and machine learning (ML) and deep learning (DL) techniques has proven beneficial in ASD detection and analysis. This paper reviews existing ML and DL models for ASD classification and prediction, examining over 60 research articles. The analysis covers both supervised and unsupervised ML methods and explores current ASD screening tests employed in laboratory diagnostics by psychologists and behavioral counselors. The review aims to provide insights into the advancements in ASD detection using data-driven approaches. It also serves as a guide for researchers focused on expanding knowledge in health informatics and medical research. Additionally, this paper discusses how mathematical, statistical, and data analytic techniques can be applied to enhance ASD data mining and self-analysis. This review supports the continuous evolution of ASD research and the development of more effective, data-supported diagnostic tools.