Recently, the integration of neural networks into robotic exoskeletons for physical rehabilitation has become popular due to their ability to interpret complex physiological signals. Surface electromyography (sEMG), electromyography (EMG), electroencephalography (EEG), and other physiological signals enable communication between the human body and robotic systems. Utilizing physiological signals for communicating with robots plays a crucial role in robot assisted neurorehabilitation. This systematic review synthesizes 44 peer-reviewed studies, exploring how neural networks can improve exoskeleton robot assisted rehabilitation for individuals with impaired upper limbs. By categorizing the studies based on robot assisted joints, sensor systems, and control methodologies, we offer a comprehensive overview of neural network applications in this field. Our findings demonstrate that neural networks, such as Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and Radial Basis Function Neural Networks (RBFNN), and other forms of neural network significantly contribute to patient specific rehabilitation by enabling adaptive learning and personalized therapy. CNNs improve motion intention estimation and control accuracy, while LSTM networks capture temporal muscle activity patterns for real-time rehabilitation. RBFNNs improve human-robot interaction by adapting to individual movement patterns, leading to more personalized and efficient therapy. This review highlights the potential of neural networks to revolutionize upper limb rehabilitation, improving motor recovery and patient outcomes in both clinical and home-based settings. It also recommends the future direction to customize existing neural networks for robot assisted rehabilitation applications.