Over the past decades, global geodynamical models have been used to investigate the thermal evolution of terrestrial planets. With the increase of computational power and improvement of numerical techniques, these models have become more complex, and simulations are now able to use a high resolution 3D spherical shell geometry and to account for strongly varying viscosity, as appropriate for mantle materials. In this study we review global 3D geodynamic models that have been used to study the thermal evolution and interior dynamics of Mars. We discuss how these models can be combined with local and global observations to constrain the planet's thermal history. In particular, we use the recent InSight estimates of the crustal thickness, upper mantle structure, and core size to show how these constraints can be combined with 3D geodynamic models to improve our understanding of the interior dynamics, present-day thermal state and temperature variations in the interior of Mars. Our results show that the crustal thickness variations control the surface heat flow and the elastic thickness pattern, as well as the location of melting zones in the present-day martian mantle. The lithospheric temperature and the seismic velocities pattern in the shallow mantle reflect the crustal thickness pattern. The large size of the martian core leads to a smaller scale convection pattern in the mantle than previously suggested. Strong mantle plumes that produce melt up to recent times become focused in Tharsis and Elysium, while weaker plumes are distributed throughout the mantle. The thickness of the seismogenic layer, where seismic events can occur, can be used to discriminate between geodynamic models, if the source depth and location of seismic events is known. Furthermore model predictions of present-day martian seismicity can be compared to the values measured by InSight. Future models need to consider recent estimates from the presentday elastic lithosphere thickness at the north pole of Mars, the effects of lateral variations of seismic velocities on waves propagation through the mantle and lithosphere, and to test the spatial distribution of seismicity by comparing model predictions to observations.