In this article, we present a comprehensive study with an experimental analysis of federated deep learning approaches for cyber security in the Internet of Things (IoT) applications. Specifically, we first provide a review of the federated learning-based security and privacy systems for several types of IoT applications, including, Industrial IoT, Edge Computing, Internet of Drones, Internet of Healthcare Things, Internet of Vehicles, etc. Second, the use of federated learning with blockchain and malware/intrusion detection systems for IoT applications is discussed. Then, we review the vulnerabilities in federated learning-based security and privacy systems. Finally, we provide an experimental analysis of federated deep learning with three deep learning approaches, namely, Recurrent Neural Network (RNN), Convolutional Neural Network (CNN), and Deep Neural Network (DNN). For each deep learning model, we study the performance of centralized and federated learning under three new real IoT traffic datasets, namely, the Bot-IoT dataset, the MQTTset dataset, and the TON_IoT dataset. The goal of this article is to provide important information on federated deep learning approaches with emerging technologies for cyber security. In addition, it demonstrates that federated deep learning approaches outperform the classic/centralized versions of machine learning (non-federated learning) in assuring the privacy of IoT device data and provide the higher accuracy in detecting attacks.