Whether it is for personal use or for medical application, wearable sensors are becoming more and more widespread. This is the industry answer to two parallel trends. First, the public show a wish to collect data about their own lifestyle. This rather new effect appeared with the rise of smartphones, smartwatches and other heart-rate belts for athletes, with the promise of understanding and improving their health and performance. From a medical point-of-view, these commercial devices are not usable because their results come from an unproven algorithm, far from clinical trials. However, the health-care professionals see a strong benefit of having trustworthy wearable devices, which can be used by their patients for extended periods of time. Having in situ medical-grade data collection is able to give insights about the patient's health status and its development. There are however limitations to what can be performed. Ideally, such a device should record as many data as possible, without requiring any set-up nor maintenance. Because of technical limitations, there are choices to be made. For example, which signals are captured, or what should be the minimal battery life? Any additional burden put on the patient hinders using the device, especially in the case of a non immediate life-threatening situation such as a daily screening. State-of-the-art biomedical wearable devices deploy multiple strategies to match the specification's stringent requirements. First it is engetically expensive to sense signals. The more data is collected, the smaller the battery lifetime. Therefore, extensive research is pursued beforehand to minimize the number of signals required. If a pathology can be reliably identified with fewer data, it is a meaningful saving. Additional energy savings are possible by minimizing the amount of data to transmit. Pushing this idea to the extreme, if the diagnostics algorithm can be efficiently run on the device itself, sending only the results is an excellent approach adopted by a number of sensor nodes. In this thesis, I first propose event-driven approaches for sensing bio-signals, designed to take into account the signal's behavior. Changing the sampling strategy is based on the fact that oversampling is frequent, because this approach provides strong guarantees about the data quality. However, it is not taking into account the actual signal's temporal characteristics, where a constant value is digitized with the same rate as a high-frequency pattern. Taking into account the signal's evolution, several kinds of events are envisioned for triggering the measure, from a simple level-crossing strategy to a more refined knowledge-based one. This event-driven sampling paradigm minimizes the amount of data to process, leading to an increased battery lifetime. Secondly, I consider a widespread but under-diagnosed disease: obstructive sleep apnea. This disease is connected to increased risks of cardiovascular diseases, motivating the need for diagnostic and treatment. The target device I consider is an existing wearable biomedical node. Following the optimization process described previously, I rely on a single biological signal processed directly on the sensor. Using machine learning, a limited number of features are extracted and filtered before being used for the obstructive sleep apnea assessment. Afterwards, the device only requires to send the results to a base station, being a non-instrusive OSA screening system.