While Synthetic Data Generation (SDG) is widely recognized in healthcare, especially for structured tabular data, longitudinal and time series data represent another crucial application. This rapid literature review analyzed 338 articles retrieved from PubMed and swisscovery, identifying and categorizing 14 prominent methods for generating synthetic longitudinal and time series health data. These methods encompass Generative Adversarial Networks (GANs), diffusion models, Variational Autoencoders (VAEs), transformer-based models, and Bayesian statistical methods. The review offers preliminary insights into the approaches’ utility, fidelity, and privacy implications, guiding future method development and adequate SDG model selection.