Stars are born with discs that during their initial stages of formation are relatively massive, asymmetric and they are being fed with material from their parent clouds. ALMA observations have revealed young discs with multiple gaps and discs with spiral structures. Such features may be due to forming planets, raising the exciting possibility that planets and planetary systems may form much faster than it has been previously thought. I will discuss whether gravitational instabilities may be responsible for the fast formation of planet-seeds in early-phase protostellar discs. I will also discuss how young planet-seeds evolve when they form within relatively massive discs, and I will argue that their fate is quite diverse, depending on the detailed physics of their interactions with their parent discs.