Smart cities are urban areas that utilize digital solutions to enhance the efficiency of conventional networks and services for sustainable growth, optimized resource management, and the well-being of its residents. Today, with the increase in urban populations worldwide, their importance is greater than ever before and, as a result, they are being rapidly developed to meet the varying needs of their inhabitants. The Internet of Things (IoT) lies at the heart of such efforts, as it allows for large amounts of data to be collected and subsequently used in intelligent ways that contribute to smart city goals. Time-series forecasting using deep learning has been a major research focus due to its significance in many real-world applications in key sectors, such as medicine, climate, retail, finance, and more. This review focuses on describing the most prominent deep learning time-series forecasting methods and their application to six smart city domains, and more specifically, on problems of a multivariate nature, where more than one IoT time series is involved.