Spatial information that exceeds the classical resolution limit by a factor of two can be made visible in the widefield fluorescence microscope by illuminating the sample with spatially structured (patterned) excitation light. By computationally restoring this information to its proper location in reciprocal space, an image with twice the normal lateral resolution can be produced. The method can be applied in three dimensions, and yields an axial sectioning power equal to that of confocal microscopes. Unlike the case in confocal microscopy, however, both the lateral and axial resolution enhancements are achieved without any loss of emission light, resulting in uncompromised sensitivity. The method has been experimentally verified on both test objects and complex biological structures and performs in complete agreement with theoretical predictions. The resulting images possess a visual clarity that dramatically exceeds that of both conventional and confocal microscopes.