Vector fields whose flow preserve the conformal class of a metric are well studied objects in conformal geometry. We will present some well-known properties of these vector fields on Riemannian manifolds and additionally their "spinorial" counterpart (also known as twistor spinors) will be constructed on Riemannian spin manifolds. For this, the Dirac and twistor operators need to be defined. Important result will be brielfy mentioned and if time permits some easy explicit examples will be given. tba