The so-called Internet of Things (IoT) aims at connecting every single object to the Internet with the purpose to automate every aspect of daily life. The IoT relies heavily on wireless low-power and lossy networks (LLNs) that collect information from the physical world and send the measurements to data aggregation and processing nodes. Most LLNs operate in the non-licensed industrial, scientific, and medical radio band, which is shared by a considerable number of systems. Coexisting wireless systems cause interference to each other, limiting their achievable performance. Multichannel communications enable frequency diversity, which in turn provides robustness against interference as well as increased network capacity. There is a considerable interest in multichannel medium access control (MAC) protocols for LLNs, including an evolving standard for the MAC layer of LLNs. In this paper, we review the latest advances in the topic and introduce a new classification framework for multichannel MAC protocols for LLNs. While our framework builds on previous review and classification studies, it adds aspects of a MAC protocol that reflect its interactions with the surrounding network stack. Seeing the resource constraints of the LLN devices, the study of such interactions—which is missing in prior classification efforts—can be the key for improving future designs. Relevant protocols published since 2006 are discussed and classified using the presented framework, including the recent multichannel MAC protocols for LLNs, such as the latest version of the IEEE 802.15.4 standard for time slotted channel hopping.