In the last few years there has been cumulative evidence showing that massive galaxies have dramatically grown in size since z~3. This result has remained very controversial as it seems at odd with our previous knowledge based on the detailed analysis of the stellar populations of nearby massive spheroids which shows that their stars were form very early on and over a short time interval. In addition to this, there is growing observational support for a significant evolution of the morphologies of these galaxies with cosmic time. In this talk, I will summarize what we have learned since the discovery of the strong evolution of the morphological properties of the massive galaxies, the mechanisms proposed to explain their origin and size increase, and the pending questions still to solve.