Imaging and sensing applications based on pulsed terahertz radiation have opened new possibilities for scientific and industrial applications. Many exploit the unique features of the terahertz (THz) spectral region, where common packaging materials are transparent and many chemical compounds show characteristic absorptions. Because of their diffraction limit, THz far-field imaging techniques lack microscopic resolution and, if subwavelength features have to be resolved, near-field techniques are required. Here, we present a THz near-field microscopy approach based on photoconductive antennas as the THz emitter and as a near-field probe. Our system allows us to measure amplitude, phase, and polarization of the electric fields in the vicinity of a sample with a spatial resolution on the micrometer scale (approximately lambda/20). Using a dielectric (plant leaf) and a metallic structure (microwire) as examples, we demonstrate the capabilities of our approach.