The Internet of Things (IoT) is rapidly changing the way in which we engage with technology on a daily basis. The IoT paradigm enables low-resource devices to intercommunicate in a fully flexible and pervasive manner, and the data from these devices is used for decision-making in critical applications such as; traffic infrastructure, health-care and home security, to name but a few. Due to the scarce resources available in these IoT devices, being able to quantify the reliability of them is a critical function. This report presents a detailed evolution of the area of reliability measurement, followed by an in-depth review of the state-of-the-art for quantification of reliability in the IoT, revealing the many challenges associated with this task. From this in-depth review, a set of key research directions for IoT reliability is determined. Despite the critical nature of the research area, at this current moment, this study is the first detailed review available in the area of assessing IoT reliability.