Biosignals often have to be detected in sports or for medical reasons. Typical biosignals are pulse and ECG (electrocardiogram), breathing, blood pressure, skin temperature, oxygen saturation, bioimpedance, etc. Typically, scientists attempt to measure these biosignals noninvasively, i.e., with electrodes or other sensors, detecting electric signals, measuring optical or chemical information. While short-time measurements or monitoring of patients in a hospital can be performed by systems based on common rigid electrodes, usually containing a large amount of wiring, long-term measurements on mobile patients or athletes necessitate other equipment. Here, textile-based sensors and textile-integrated data connections are preferred to avoid skin irritations and other unnecessary limitations of the monitored person. In this review, we give an overview of recent progress in textile-based electrodes for electrical measurements and new developments in textile-based chemical and other sensors for detection and monitoring of biosignals.