Medical monitors have benefited from technological advances in the field of wireless communication, processing and power sources. These advances have made possible miniaturization and prolonged operating times of medical monitors, as well as their global integration into telemedical systems. This allows patients to have real-time feedback about medical conditions while going about their normal daily activities. System designers are facing specific issues related to monitor acceptability, application requirements, power consumption and system connectivity. In this paper we discuss system design issues, present a survey of existing systems and sensors, and introduce two taxonomies of medical monitoring applications for wearable computing.