We recall Greenberg's programme to generalize Iwasawa theory via Galois deformations, which appeared in his paper published in 1994. After speaking on general problems around this programme, I would like to report on some current results regarding nearly ordinary deformations over the rational number field. If time allows, I would like to state some open questions related to Galois representations into large p-adic rings, Euler systems for Galois deformations, etc.