In recent years, the interest in medical monitoring for human health has been rapidly increasing due to widespread concern. Hydrogels are widely used in medical monitoring and other fields due to their excellent mechanical properties, electrical conductivity and adhesion. However, some of the non-degradable materials in hydrogels may cause some environmental damage and resource waste. Therefore, organic renewable natural polymers with excellent properties of biocompatibility, biodegradability, low cost and non-toxicity are expected to serve as an alternative to those non-degradable materials, and also provide a broad application prospect for the development of natural-polymer-based hydrogels as flexible electronic devices. This paper reviews the progress of research on many different types of natural-polymer-based hydrogels such as proteins and polysaccharides. The applications of natural-polymer-based hydrogels in body movement detection and biomedical monitoring are then discussed. Finally, the present challenges and future prospects of natural polymer-based hydrogels are summarized.