Magnetotelluric (MT) studies represent the structure of crust and mantle in terms of conductivity anomalies, while geodynamic modelling predicts the deformation and evolution of crust and mantle subject to plate tectonic processes. Here, we review the first attempts to link MT models with geodynamic models. An integration of MT with geodynamic modelling requires the use of relationships between conductivity and rheological parameters such as viscosity and melt fraction, which are provided by laboratory measurements of rock properties. Owing to present limitations in our understanding of these relationships, and in interpreting the trade-off between scale and magnitude of conductivity anomalies from MT inversions, most studies linking MT and geodynamic models are qualitative rather than providing hard constraints. Some recent examples attempt a more quantitative comparison, such as a study from the Himalayan continental collision zone, where rheological parameters have been calculated from a resistivity model and compared to predictions from geodynamic modelling. We conclude by demonstrating the potential in combining MT results and geodynamic modelling with examples that directly use MT results as constraints within geodynamic models of ore bodies and studies of an active volcano-tectonic rift.