We describe ultraresolution microscopy far beyond the classical Abbe diffraction limit of one half wavelength (λ/2), and also beyond the practical limit (ca. λ/10) of aperture–based scanning near–field optical microscopy (SNOM). The ‘apertureless’ SNOM discussed here uses light scattering from a sharp tip (hence scattering–type or s–SNOM) and has no λ–related resolution limit. Rather, its resolution is approximately equal to the radius a of the probing tip (for commercial tips, a<20 nm) so that 10 nm is obtained in the visible (λ/60). A resolution of λ/500 has been obtained in the mid–infrared at λ=10 μm. The advantage of infrared, terahertz and even microwave illumination is that specific excitations can be exploited to yield specific contrast, e.g. the molecular vibration offering a spectroscopic fingerprint to identify chemical composition. S–SNOM can routinely acquire simultaneous amplitude and phase images to obtain information on refractive and absorptive properties. Plasmon– or phonon–resonant materials can be highlighted by their particularly high near–field signal level. Furthermore, s–SNOM can map the characteristic optical eigenfields of small, optically resonant particles. Lastly, we describe theoretical modelling that explains and predicts s–SNOM contrast on the basis of the local dielectric function.