Although grain growth (GG) mechanisms are known for more than one century and actively studied for 70 years, it remains a very hot research topic in terms of in-situ data acquisition, involved equations, and modeling. This historical background has brought us to the current global picture: GG in single-phase polycrystals relatively free of point and line defects is driven by the minimization of grain boundary (GB) areas in order to decrease the total interfacial energy of the polycrystal. The velocity $V$ at which GBs move when subjected to a driving pressure is assumed to be the product of the GB mobility $M$ and $P$. In GG context, the pressure, $P$, is the product of the GB energy $\gamma$ and the GB curvature, i.e., the trace of the curvature tensor in the 3D space, $\kappa$. This expression is essential in the context of nickel-base superalloys as it also historically explained the Smith-Zener effect due to the abrupt evolution of the GB curvature when a second phase particle is encountered by a migrating GB.

The recent improvements of GG experiments now make it possible to precisely discuss the velocity equation in the state of the art. In particular, non destructive in-situ experiments in a synchrotron by 3D X-ray diffraction microscopy techniques, allow to avoid bias inherent to 2D observations and open the path to precise reverse engineering to discuss the $V/\kappa$ ratio. The interpretation of these recent results tends to refute or at least to question the real impact of curvature on the kinetics of the GBs or to dispel the 5-parameter description of the reduced mobility ($M\gamma$ product). 

Using a new full-field framework, which considers a 5-parameter description of the reduced mobility and torque terms at multiple junctions, it will be illustrated how topological and torque effects can complicate GB dynamics and so weigh the current discussion concerning the validity or invalidity of $V=MP$ equation for GG at the mesoscopic scale.