This thesis is split into two broad sections. These are defined by the various applications of scattering-type near-field optical microscopy (s-SNOM) in different parts of the electromagnetic spectrum; the near-infrared (700 - 1000nm) and the mid-infrared (6 - 10um). S-SNOM is a means of imaging surfaces at resolutions well below the diffraction limit - the level of recorded detail does not depend on the wavelength of light (as it does with traditional optical microscopy), but instead on the sharpness of a probe (usually around 10nm), meaning an image resolution approaching a thousandth of a wavelength in the mid-infrared. For the work presented in the near-infrared, the focus lies with the modelling and mapping of various plasmonic resonances supported by metallic nanostructures. These resonances have the ability to "squeeze" light into substantially sub-wavelength volumes which is useful for a variety of applications ranging from cancer treatments to molecular sensing. The mid-infrared section starts with the implementation of a pulsed quantum cascade laser (QCL) as the system's light source. This presents some instrumentation challenges as all s-SNOM imaging to date has been conducted with continuous-wave (CW) lasers. Using a pulsed laser also raises some significant signal-to-noise implications which are quantified and discussed. In terms of the experimental applications of such a setup, the first steps towards ultra-high resolution infrared chemical spectroscopy are made by studying the epithelial cells of an oesophageal biopsy. The thesis concludes with an examination of the major noise sources faced by s-SNOM, and makes a number of recommendations on how their effects can be mitigated.