Autism spectrum disorder (ASD) is a neurodevelopmental disorder associated with impairments in social and lingual abilities. The current gold standard for diagnosis is the autism diagnostic observation schedule (ADOS) combined with expert clinical judgement. The actual cause for autism is still unknown. Early ASD diagnosis is critical for conducting personalized treatment plans and can lead to significant development enhancements. Machine learning techniques, especially deep learning, have been widely incorporated in attempts to develop objective computer-aided technologies to diagnose autism with brain imaging modalities. Task-based functional magnetic resonance imaging (TfMRI) is a brain imaging modality that reveals functional activity of the brain in response to different experiments to study the effects of a brain disease or disorder. This study provides a comprehensive review of research that deploys traditional machine learning and deep learning techniques in diagnosing ASD based on TfMRI. Classification results manifest that TfMRI holds early autism biomarkers and suggests future research to establish multi-modal studies that integrate TfMRI with structural, functional, clinical and gnomic data with higher number of participating subjects.