Twistorial structures revisited

We review the twistorial structures by providing a setting under which the corresponding (differential) geometry can be described, by involving the $\rho$-connections. This applies, for example, to give new proofs of the existence of the relevant connections for the projective and the quaternionic geometries. Along the way, we show that, in this setting, the Ward transformation is a consequence of the good behaviour of the $\rho$-connections, under pull back.