[en] I discuss a recently unveiled feature in the dynamics of two dimensional coarsening systems on the lattice with Ising symmetry: they first approach a critical percolating state via the growth of a new length scale, and only later enter the usual dynamic scaling regime. The time needed to reach the critical percolating state diverges with the system size. These observations are common to Glauber, Kawasaki, and voter dynamics in pure and weakly disordered systems. An extended version of this account appeared in 2016 C. R. Phys . . I refer to the relevant publications for details. (special issue on statphys 26)