In the current network-based computing world, where the number of interconnected devices grows exponentially, their diversity, malfunctions, and cybersecurity threats are increasing at the same rate. To guarantee the correct functioning and performance of novel environments such as Smart Cities, Industry 4.0, or crowdsensing, it is crucial to identify the capabilities of their devices (e.g., sensors, actuators) and detect potential misbehavior that may arise due to cyberattacks, system faults, or misconfigurations. With this goal in mind, a promising research field emerged focusing on creating and managing fingerprints that model the behavior of both the device actions and its components. The article at hand studies the recent growth of the device behavior fingerprinting field in terms of application scenarios, behavioral sources, and processing and evaluation techniques. First, it performs a comprehensive review of the device types, behavioral data, and processing and evaluation techniques used by the most recent and representative research works dealing with two major scenarios: device identification and device misbehavior detection. After that, each work is deeply analyzed and compared, emphasizing its characteristics, advantages, and limitations. This article also provides researchers with a review of the most relevant characteristics of existing datasets as most of the novel processing techniques are based on machine learning and deep learning. Finally, it studies the evolution of these two scenarios in recent years, providing lessons learned, current trends, and future research challenges to guide new solutions in the area.