Until a safe and effective vaccine to fight the SARS-CoV-2 virus is developed and available for the global population, preventive measures, such as wearable tracking and monitoring systems supported by Internet of Things (IoT) infrastructures, are valuable tools for containing the pandemic. In this review paper we analyze innovative wearable systems for limiting the virus spread, early detection of the first symptoms of the coronavirus disease COVID-19 infection, and remote monitoring of the health conditions of infected patients during the quarantine. The attention is focused on systems allowing quick user screening through ready-to-use hardware and software components. Such sensor-based systems monitor the principal vital signs, detect symptoms related to COVID-19 early, and alert patients and medical staff. Novel wearable devices for complying with social distancing rules and limiting interpersonal contagion (such as smart masks) are investigated and analyzed. In addition, an overview of implantable devices for monitoring the effects of COVID-19 on the cardiovascular system is presented. Then we report an overview of tracing strategies and technologies for containing the COVID-19 pandemic based on IoT technologies, wearable devices, and cloud computing. In detail, we demonstrate the potential of radio frequency based signal technology, including Bluetooth Low Energy (BLE), Wi-Fi, and radio frequency identification (RFID), often combined with Apps and cloud technology. Finally, critical analysis and comparisons of the different discussed solutions are presented, highlighting their potential and providing new insights for developing innovative tools for facing future pandemics.