The Internet of Things (IoT) is seeing significant growth, as the quantity of interconnected devices in communication networks is on the rise. The increased connectivity of devices has heightened their susceptibility to hackers, underscoring the need to safeguard IoT devices. This research investigates cybersecurity in the context of the Internet of Medical Things (IoMT), which encompasses the cybersecurity mechanisms used for various healthcare devices connected to the system. This study seeks to provide a concise overview of several artificial intelligence (AI)-based methodologies and techniques, as well as examining the associated solution approaches used in cybersecurity for healthcare systems. The analyzed methodologies are further categorized into four groups: machine learning (ML) techniques, deep learning (DL) techniques, a combination of ML and DL techniques, Transformer-based techniques, and other state-of-the-art techniques, including graph-based methods and blockchain methods. In addition, this article presents a detailed description of the benchmark datasets that are recommended for use in intrusion detection systems (IDS) for both IoT and IoMT networks. Moreover, a detailed description of the primary evaluation metrics used in the analysis of the discussed models is provided. Ultimately, this study thoroughly examines and analyzes the features and practicality of several cybersecurity models, while also emphasizing recent research directions.