Summary The biomechanics of stomatal movements have fascinated scientists for almost 150 yr, yet we still lack a conclusive and coherent mechanistic understanding of the process. In this review, we present a framework that allows critical insight into the state of knowledge of stomatal biomechanics, with a focus on modelling approaches. We apply the framework in two ways. First, contextualising the history, we show how the nature and function of models of stomatal mechanics have evolved. Second, we use the framework to appraise three key features of extant models: cell wall mechanical properties, guard cell shape, and the role of surrounding epidermal cells. We evaluate the empirical origin and model representations of these features, summarising how each is currently thought to explain stomatal function, while also identifying limitations in our understanding. We propose that a better appreciation of gaps in knowledge in the empirical domain, particularly the actual shifts in cell shape during stomatal response, combined with careful reinterpretation of existing data, will lead to new insight and a more complete understanding of stomatal mechanics.