The coarsening behaviour of coherent precipitates and particularly of gamma-prime (γ′) precipitates in Ni-base alloys is reviewed. In such elastically constrained systems, strange coarsening phenomena sometimes appear, e.g. the deceleration of coarsening, the split of a single particle into a doublet or an octet, etc. Such unbelievable phenomena can clearly be explained by introducing new coarsening theories like the Bifurcation theory in which the elasticity effect and particularly the effect of elastic interaction energy between particles are incorporated into the driving force for coarsening. Not only the surface energy but also the elastic interaction energy really plays an essential role in the formation and the stability of various precipitate morphology including coarsening.