Physiological signals obtained from electroencephalography (EEG), electromyography (EMG), and electrocardiography (ECG) provide valuable clinical information but pose challenges for analysis due to their high-dimensional nature. Traditional machine learning techniques, relying on hand-crafted features from fixed analysis windows, can lead to the loss of discriminative information. Recent studies have demonstrated the effectiveness of deep convolutional neural networks (CNNs) for robust automated feature learning from raw physiological signals. However, standard CNN architectures require two-dimensional image data as input. This has motivated research into innovative signal-to-image (STI) transformation techniques to convert one-dimensional time series into images preserving spectral, spatial, and temporal characteristics. This paper reviews recent advances in strategies for physiological signal-to-image conversion and their applications using CNNs for automated processing tasks. A systematic analysis of EEG, EMG, and ECG signal transformation and CNN-based analysis techniques spanning diverse applications, including brain-computer interfaces, seizure detection, motor control, sleep stage classification, arrhythmia detection, and more, are presented. Key insights are synthesized regarding the relative merits of different transformation approaches, CNN model architectures, training procedures, and benchmark performance. Current challenges and promising research directions at the intersection of deep learning and physiological signal processing are discussed. This review aims to catalyze continued innovations in effective end-to-end systems for clinically relevant information extraction from multidimensional physiological data using convolutional neural networks by providing a comprehensive overview of state-of-the-art techniques.