Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by communication barriers, societal disengagement, and monotonous actions. Traditional diagnostic methods for ASD rely on clinical observations and behavioural assessments, which are time -consuming. In recent years, researchers have focused mainly on the early diagnosis of ASD due to the unavailability of recognised causes and the lack of permanent curative solutions. Electroencephalography (EEG) research in ASD offers insight into the neural dynamics of affected individuals. This comprehensive review examines the unique integration of EEG, machine learning, and statistical analysis for ASD identification, highlighting the promise of an interdisciplinary approach for enhancing diagnostic precision. The comparative analysis of publicly available EEG datasets for ASD, along with local data acquisition methods and their technicalities, is presented in this paper. This study also compares preprocessing techniques, and feature extraction methods, followed by classification models and statistical analysis which are discussed in detail. In addition, it briefly touches upon comparisons with other modalities to contextualize the extensiveness of ASD research. Moreover, by outlining research gaps and future directions, this work aims to catalyse further exploration in the field, with the main goal of facilitating more efficient and effective early identification methods that may be helpful to the lives of ASD individuals.