Internet of Things (IoT) is considered as a huge network of objects or things, capable to communicate data among these things or from one object to any other device/system connected through internet. The term “thing” may contain a sensor, is run through software, or is influenced by any other tools through which it can capture, process, or analyse the data. The generated data in any IoT device or network is enormous, structured or unstructured, unimodal or multimodal, and temporal or sequential, and it should be processed effectively and efficiently for capturing and transmitting the meaningful information rapidly to any other device/thing. Deep Learning can be considered as a branch of Machine Learning, heavily adopted by the research communities due to its huge data handling and processing capability. Various deep learning models such as Convolutional Neural Networks, Recurrent Neural Networks, and its architectural variants such as Long Short-Term Memory and Gated Recurrent Unit are useful for better feature extraction from unimodal or multimodal data. Due to enhanced computational capabilities of various devices with the help of high-end computers or accelerators, it has become useful to run the aforementioned deep models on this huge amount of data. With the advent of Deep Learning and IoT, breakthrough achievements by various IoT applications have been observed using deep learning models in various domains such as healthcare, smart homes, smart cities, smart transportation, and many more. Herein, we present issues, challenges, role, and applicability of deep learning models in various IoT devices and applications in the aforementioned domains with an emphasis on healthcare domain. However, other domains are also covered in brief. Moreover, in addition to the aforementioned mainstream deep models, we also brief the role and applicability of other deep models such as Auto encoders, Recursive Boltzmann Machine, and Adversarial Networks in various IoT applications. In addition, we present the architectural advancements of mainstream deep models as the future research direction to leverage the performance improvements in various IoT devices and applications.