In recent years a significant development of BASN (Body Area Sensor Networks) as a special subclass of WSN (Wireless Sensor Networks) has emerged. These networks have enabled a rapid development of telemedicine systems, which provide remote monitoring of patients and their vital parameters. The article gives a short overview of the BASN networks. Furthermore, a general system architecture of telemedicine systems is proposed. The proposed architecture includes a local sensory area, a communication network area and an institutional network area. It also provides the security and privacy of patient-related data. Furthermore, the article surveys some existing telemedicine systems. Finally, some current problems are explained and the directions for the future development of the telemedicine systems are given.