In this review we describe fundamentals of scanning near-field optical microscopy with aperture probes. After the discussion of instrumentation and probe fabrication, aspects of light propagation in metal-coated, tapered optical fibers are considered. This includes transmission properties and field distributions in the vicinity of subwavelength apertures. Furthermore, the near-field optical image formation mechanism is analyzed with special emphasis on potential sources of artifacts. To underline the prospects of the technique, selected applications including amplitude and phase contrast imaging, fluorescence imaging, and Raman spectroscopy, as well as near-field optical desorption, are presented. These examples demonstrate that scanning near-field optical microscopy is no longer an exotic method but has matured into a valuable tool.