The analysis of biomedical signals is a very challenging task. This review paper is focused on the presentation of various methods where biomedical data, in particular vital signs, could be monitored using sensors mounted to beds. The presented methods to monitor vital signs include those combined with optical fibers, camera systems, pressure sensors, or other sensors, which may provide more efficient patient bed monitoring results. This work also covers the aspects of interference occurrence in the above-mentioned signals and sleep quality monitoring, which play a very important role in the analysis of biomedical signals and the choice of appropriate signal-processing methods. The provided information will help various researchers to understand the importance of vital sign monitoring and will be a thorough and up-to-date summary of these methods. It will also be a foundation for further enhancement of these methods.