In the dynamic realm of technology, the pervasive influence of the Internet of Things (IoT) continues its transformative journey, reshaping established paradigms. The imperative for secure key agreement protocols has escalated, becoming a consequential focal point. Regrettably, prevailing classification schemes for these protocols frequently fall short in terms of desired comprehensiveness and often neglect specific application contexts. A significant challenge within this domain arises from the insufficient consideration of the distinctive physical limitations and infrastructure inherent in IoT environments. This oversight has given rise to a proliferation of diverse, yet frequently unsuitable, key exchange methods. This paper addresses these pressing challenges through the presentation of a novel methodology for classifying key agreement methods, finely tuned to meet the unique demands of the IoT landscape. Our approach introduces four meticulously crafted classifications, each designed to augment our understanding of these methods based on key criteria: the protocol process, protocol features and capabilities, resource requirements, and communication models. Through the lens of these comprehensive classifications, we endeavor to provide a more nuanced perspective on IoT key agreement protocols. This encompasses insights into their suitability for diverse applications and their alignment with the intrinsic constraints of IoT environments. Employing this multidimensional classification framework, our research contributes to a profound exploration of IoT security and key agreement methods. This, in turn, offers invaluable insights for researchers, practitioners, and decision-makers navigating the dynamic landscape of the Internet of Things.