Since the 1970s, numerous global plate tectonic models have been proposed to reconstruct the Earth's evolution through deep time. The reconstructions have proven immensely useful for the scientific community. However, we are now at a time when plate tectonic models must take a new step forward. There are two types of reconstructions: those using a 'single control' approach and those with a 'dual control' approach. Models using the 'single control' approach compile quantitative and/or semi-quantitative data from the present-day world and transfer them to the chosen time slices back in time. The reconstructions focus therefore on the position of tectonic elements but may ignore (partially or entirely) tectonic plates and in particular closed tectonic plate boundaries. For the readers, continents seem to float on the Earth's surface. Hence, the resulting maps look closer to what Alfred Wegener did in the early twentieth century and confuse many people, particularly the general public. With the 'dual control' approach, not only are data from the present-day world transferred back to the chosen time slices, but closed plate tectonic boundaries are defined iteratively from one reconstruction to the next. Thus, reconstructions benefit from the wealth of the plate tectonic theory. They are physically coherent and are suited to the new frontier of global reconstruction: the coupling of plate tectonic models with other global models. A joint effort of the whole community of geosciences will surely be necessary to develop the next generation of plate tectonic models.