Higher-spin fields can play an important role in effective field theories and increasingly are of interest due to their appearance in recent studies of holography. Understanding their interactions is however often involved and searching for alternative formulations could be very useful. In this talk we will consider one such formulation, namely twistors. After giving a general introduction to the use of twistors in describing the dynamics of massless field theories, we will focus on the construction of off-shell actions directly in twistor space including a recent higher-spin generalisation of self-dual Weyl gravity. We will show how this formulation produces the expected flat space-time spectrum and linearised symmetries. In analogy with the known embedding of Einstein gravity inside Weyl gravity, we identify a ghost free sub-sector of the conformal higher-spin theory and consider its cubic couplings. Finally we describe proposed anti-self-dual interaction terms to extend the twistor action to the full conformal higher-spin theory.