Vectorial vortices obtained with quantized Pancharatnam-Berry phase optical elements (PBOEs) are presented. A vectorial vortex occurs around a point where a scalar vortex is centered in at least one of the scalar components of the vectorial wave field. PBOEs ulilize the geometric phase that accompanies space-variant polarization manipulations to achieve a desired phase modification. The geometric phase is formed through the use of discrete computer-generated space-variant subwavelength dielectric gratings. By discretely controlling the local grating orientation, we could form complex vectorial fields. Propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry were experimentally demonstrated. Moreover, a new class of vectorial vortices based on coherent addition of two orthogonal circular polarized Bessel beams of identical order, but with different propagation constant is presented. The transversely space-variant axially symmetric polarization distributions of these vectorial fields rotate as they propagate while still maintaining a propagation-invariant Bessel intensity distribution. The polarization properties were verified by both full space-variant polarization analysis and measurements. Rotating intensity patterns were also demonstrated by transmitting the vectorial vortices through a linear polarizer. V.