Large departures from standard L-mode confinement scaling laws are now being observed in most tokamaks which appear promising for relaxing the plasma current constraint and therefore open the route to high performance steady-state operation with high bootstrap current fraction. Prospects of the weak or reversed magnetic shear scenarios for steady-state tokamak operation are presented in the light of recent experimental progress to control pressure and current profiles with the combined use of various heating and current drive schemes. Implications of the present experiments on the modelling of future non-inductive operation in existing tokamaks and in ITER are addressed.