This thesis focuses on two different approaches of beating the diffraction limit in the mid-infrared. One approach uses scattering-type scanning near-field optical microscopy (s-SNOM) to map the optical response of a sample surface with < 10 nm resolution. By utilising the recent development of widely tuneable quantum cascade lasers (QCL), this work experimentally investigates two distinct applications. The first maps out the dispersion of plasmons in graphene to determine the local Fermi energy with high accuracy. In addition, novel plasmon focusing phenomena are presented at interfaces between single and bilayer graphene. The second experimental application uses infrared s-SNOM to image, for the first time, the ultrastructure inside individual human cells with ~8 nm resolution. Furthermore, nanoscale infrared spectroscopy is used to map out the location of a clinically relevant anti-cancer drug within a single cell without chemical labelling, for the first time. The final part of this thesis comprises a theoretical study of metamaterial superlenses, which allow for deeply sub-wavelength spatial resolution to be preserved. The insights gained here led to the development of a novel infrared superlens that is shown to improve the distance at which sub-diffraction limited (< λ/15) features are preserved by a factor of 25 over previous designs.