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Autism Spectrum Disorder (ASD) is a multifaceted neurodevelopmental disorder that presents with difficulties in social interaction, communication, and repetitive behavior. Accurate and early diagnosis is vital for effective intervention. Functional Magnetic Resonance Imaging (fMRI) has been an important tool to investigate the neural correlates of ASD. Recent deep learning advancements, especially transformer-based models, have proven useful for processing fMRI data for ASD detection. This review paper offers a general overview of transformer architectures for fMRI-based ASD classification. We address several methodologies, including spatial-temporal transformers, graph transformers, and mixed models combining convolutional neural networks (CNNs) and transformers. Prominent studies, such as the STAR Former model, showcase the success of both spatial and temporal features of BOLD signals being captured by novel modules such as eigenvector centrality-based ROI analysis and multiscale attention mechanisms. Nevertheless, despite these improvements, issues still persist, such as requiring large amounts of data to avoid overfitting and combining multimodal data to increase accuracy. This review will focus on outlining the current state-of-the-art transformer-based methods in fMRI-based ASD detection, identifying their advantages and disadvantages, and providing future directions to improve the field.