This paper aims to review some deep learning-based methods for the classification of functional Magnetic Resonance Imaging (fMRI) brain images. fMRI is one of the MRI modalities which provides information about the activity of the neurons in the brain. In particular, the fMRI signal is sensitive to blood dynamic changes, which drive the neuron firing. This relationship is known as the Blood Oxygenation Level Dependent (BOLD) effect. Two main applications are possible: a task-specific activity and a resting state. The main difference is that in the first case, a patient is asked to perform a specific task, and the fMRI shows the brain response, while in the resting state, no particular action is required. The study of brain activity and response represents one of the significant research challenges to understand diseases and potential damages better. Using automated techniques based on artificial intelligence, such as machine learning or deep learning, allow the analysis of large fMRI datasets. The classification task is essential because it enables the possibility to support the decision-making process by healthcare experts by identifying particular diseases from images. This paper reviews deep learning methods for fMRI classification, their corresponding accuracies, and the required computational resources for massive fMRI datasets.