In this paper, we present a systematic literature review on deep generative models for physiological signals, particularly electrocardiogram (ECG), electroencephalogram (EEG), photoplethysmogram (PPG) and electromyogram (EMG). Compared to the existing review papers, we present the first review that summarizes the recent state-of-the-art deep generative models. By analyzing the state-of-the-art research related to deep generative models along with their main applications and challenges, this review contributes to the overall understanding of these models applied to physiological signals. Additionally, by highlighting the employed evaluation protocol and the most used physiological databases, this review facilitates the assessment and benchmarking of deep generative models.