This thesis studies apertureless Scanning Near Field Optical Microscopy, a technique that uses the apex of a very sharp tip to obtain local optical information with lateral resolution much beyond the diffraction limit. Both theoretical and experimental results are discussed. The theoretical work is a significant advance towards the quantitative convergence of experiments and theoretical predictions, and should be useful in aiding the interpretation of measured images. Extended tips and substrates are used, and the detector is also carefully modeled. A static tip in vacuum serves to study the influence of the tip and illumination geometry on the far fields and on the near fields in the proximity of the tip apex, the volume used to probe the sample. Including a gold substrate and the commonly used demodulation scheme allows to study the discrimination of the components carrying the local information. A very good discrimination is verified for silicon tips and small oscillation amplitudes, as far as the tip interacts closely with the substrate and the oscillation remains highly sinusoidal. The imaging process is studied by including patterned substrates. The obtained signal is mostly sensitive to a few nanometers of depth into the sample, and the influence of the scanning conditions on the level of signal, background suppression and lateral resolution is characterized. Further, a closer look into the behavior of the extended physical detector reveals the influence of the spatial inhomogeneities of the scattered fields and, for interferometric measurements, the large significance of the optical phase. Experimentally, different techniques are first described that can facilitate images with clear local information. A cross polarization scheme is introduced which is very useful for non-perturbative measurements. It is applied to the mapping of the the field distribution surrounding plasmonic structures, for both the phase and the amplitude. Beyond dipolar resonances, I also study coupled dipoles and quadrupole field distributions. When imaging artifacts are avoided, the obtained images closely resemble theoretical expectations.