We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally...