With the ever-growing requirements in the healthcare sector aimed at personalized diagnostics and treatment, continuous and real-time monitoring of relevant parameters is gaining significant traction. In many applications, health status monitoring may be carried out by dedicated wearable or implantable sensing devices only within a defined period and followed by sensor removal without additional risks for the patient. At the same time, disposal of the increasing number of conventional portable electronic devices with short life cycles raises serious environmental concerns due to the dangerous accumulation of electronic and chemical waste. An attractive solution to address these complex and contradictory demands is offered by biodegradable sensing devices. Such devices may be able to perform required tests within a programmed period and then disappear by safe resorption in the body or harmless degradation in the environment. This work critically assesses the design and development concepts related to biodegradable and bioresorbable sensors for healthcare applications. Different aspects are comprehensively addressed, from fundamental material properties and sensing principles to application-tailored designs, fabrication techniques, and device implementations. The emerging approaches spanning the last 5 years are emphasized and a broad insight into the most important challenges and future perspectives of biodegradable sensors in healthcare are provided.