Chronic Obstructive Pulmonary Disease (COPD) is a debilitating and life-threatening disease. In 2016 there were an estimated 251 million cases of COPD globally and the World Health Organization predicts that by 2030 COPD will be the third leading cause of death worldwide. Technologies that help people with COPD manage their condition could have significant impact on their lives. The work presented in this thesis outlines a system that uses wearable and mobile devices to passively sense and monitor patients with COPD. Mobile and wearable devices contain a myriad of sensors and have been used in applications ranging from earthquake detection to flight control for drones. To make these devices relevant for COPD monitoring, this thesis focuses on two signals that can be extracted from wearable sensors, respiratory rate and coughing. To detect respiratory rate, we propose WearBreathing -- our system for respiratory rate detection using the accelerometer and gyroscope sensors found in smartwatches. While respiratory rate from a smartwatch has been done in previous works, existing methods are only accurate in in-lab settings and while participants are stationary, making them unsuitable for remote monitoring. Therefore, WearBreathing is designed specifically to operate in the wild and we show that it is indeed more accurate in the wild than existing methods. Similar to respiratory rate, we found that existing cough detection solutions do not perform well in the wild. Using an in-the-wild dataset that we collect from COPD patients, we first characterize the sounds captured by a smartwatch microphone in a wild setting. Using our dataset, we build a state of the art cough detector, which we call CoughWatch that works on in-the-wild data and is more accurate than existing cough detectors. Finally, because mobile devices are resource constrained devices designed for intermittent use, battery life becomes a significant concern when attempting to continuously monitor sensor data. End users, such as patients with COPD, are unlikely to use a device that provides only a few hours of battery life per charge. Therefore, we propose Sidewinder, a developer friendly hardware architecture for energy efficient continuous sensing on mobile devices.