The Internet of things (IoT) is growing at a fast pace owing to its vast applications in varied fields such as medicine, society, economy, and even the military. This growth cannot continue without establishing high quality. Over the past decade, interest in research for the quality assurance of IoT has gradually grown. However, the discipline is still evolving, and further research is required to investigate the various quality-related aspects. Although assessing the entire system is impractical, to assure the quality of IoT applications, various assessment levels are required. A well-known and established approach to mitigate this difficulty is to model the entire system or a few parts of it for the sake of assessment, which is known as model-based testing. To determine what has been achieved thus far and what is lacking in this direction, this paper presents an extensive study on the use of the model-based approach to assure the quality of IoT applications. The study systematically reviews papers published from 2009 (early publications on IoT) to 2019 that reported the explicit use of models to assess the quality aspects of IoT applications. As a result of an extensive search process, the paper presents the results of scanning and reviewing 390 published papers. Thus far, out of these, 54 studies used the model-based approach to assess at least one quality aspect of an IoT application. In addition to the several relevant research questions that have been addressed in this study, this paper also presents several new insights and approaches for future research.