Data quality is a key factor in the development of trustworthy AI in healthcare. A large volume of curated datasets with controlled confounding factors can improve the accuracy, robustness, and privacy of downstream AI algorithms. However, access to high-quality datasets is limited by the technical difficulties of data acquisition, and large-scale sharing of healthcare data is hindered by strict ethical restrictions. Data synthesis algorithms, which generate data with distributions similar to real clinical data, can serve as a potential solution to address the scarcity of good quality data during the development of trustworthy AI. However, state-of-the-art data synthesis algorithms, especially deep learning algorithms, focus more on imaging data while neglecting the synthesis of non-imaging healthcare data, including clinical measurements, medical signals and waveforms, and electronic healthcare records (EHRs). Therefore, in this article, we will review synthesis algorithms, particularly for non-imaging medical data, with the aim of providing trustworthy AI in this domain. This tutorial-style review article will provide comprehensive descriptions of non-imaging medical data synthesis, covering aspects such as algorithms, evaluations, limitations, and future research directions.