The so-called “helical modes” of an electromagnetic wave are characterized by a helical shape of the wavefront. They carry quantized angular momentum of an orbital kind, as opposed to the spin-like angular momentum that can be associated with circularly polarized waves. In a way, one can consider helical modes as “twisted” light beams that are “spinning upon themselves” while propagating. In the talk I will present a novel method for generating helical waves of light by letting a circularly-polarized non-helical wave pass through an azimuthally inhomogeneous birefringent plate made of a suitably patterned liquid crystal, a device dubbed “q-plate”. The q-plate converts the variation of spin angular momentum associated with the switching of light polarization handedness into orbital angular momentum, an optical process that had not been envisioned before. Generalizing this idea, patterned birefringent plates similar to q-plates may be used for shaping the optical wavefront of a circularly polarized beam in any prescribed way. Moreover, these plates allow fast switching between conjugate wavefronts by inverting the handedness of the input polarization. Devices based on this principle have been called Pancharatnam-Berry phase optical elements.