Soft material-enabled electronics offer distinct advantage, over conventional rigid and bulky devices, for numerous wearable and implantable applications. Soft materials allow for seamless integration with skin and tissues due to enhanced mechanical flexibility and stretchability. Wearable devices, such as sensors, offer continuous, real-time monitoring of biosignals and movements, which can be applied in rehabilitation and diagnostics, among other applications. Soft implantable electronics offer similar functionalities, but with improved compatibility with human tissues. Biodegradable soft implantable electronics are also being developed for transient monitoring, such as in the weeks following surgery. To further advance soft electronics, materials, integration strategies, and fabrication techniques are being developed. This paper reviews recent progress in these areas, toward the development of soft material-enabled electronics for medicine, healthcare, and human-machine interfaces.