The study of gravitropic movements in plants has enjoyed a long history of research going back to the pioneering works of the 19th century and the famous book entitled 'The power of movement in plants' by Charles and Francis Darwin. Over the last few decades, the emphasis has shifted towards the cellular and molecular biology of gravisensing and the onset of auxin gradients across the organs. However, our understanding of plant movement cannot be completed before quantifying spatio-temporal changes in curvature and how they are produced through the motor process of active bending and controlled by gravisensing. This review sets out to show how combining approaches borrowed from continuum mechanics (kinematic imaging, structural modelling) with approaches from physiology and modern molecular biology has made it possible to generate integrative biomechanical models of the processes involved in gravitropism at several levels. The physiological and biomechanical bases are reviewed and two of the most complete integrative models of the gravireaction organ available are then compared, highlighting how the comparison between movements driven by differential growth and movements driven by reaction wood formation in woody organs has provided highly informative key insights. The advantages of these models as tools for analysing genetic control through quantitative process-based phenotyping as well as for identifying target traits for ecological studies are discussed. It is argued that such models are tools for a systems biology approach to gravitropic movement that has the potential to resolve at least some of the research questions raised 150 years ago.