The diffraction limit can be circumvented by scattering-type scanning near-field optical microscope (s-SNOM). S-SNOM is based on an atomic force microscope (AFM), where a metal tip is illuminated with a focused laser beam. The tip acts as an antenna and focuses the illumination to a nanoscale near-field spot at its apex. Near-field interaction between tip and sample modifies the tip scattered light. Interferometric detection of the tip scattered light allows for probing the local conductivity properties of the sample by recording the amplitude and phase of the scattered field. In this thesis, by taking advantage of the unique high-resolution imaging and spectroscopy capability of s-SNOM, we study the nanoscale conductivity modulation of doped semiconductor nanostructures and correlated oxides at mid-infrared and terahertz frequencies. We generated and characterized nanoscale patterns with different conductivity values on the surface of prototypical correlated perovskite oxide SmNiO3 (SNO) which were further tuned via temperature modulation and spontaneous hydrogenation. Nanoscale reconfigurable conductivity control in SNO enabled manipulation of sub-diffraction light-matter interaction and dispersion engineering of hyperbolic polaritons in van der Waals crystals, such as hexagonal boron nitride (hBN) or alpha-phase molybdenum trioxide (α-MoO3). To study nanoscale conductivity changes and quantitative sampling of carrier densities in semiconductor nano-structures (nanowires and p-n junctions), we combined for the first time in this thesis s-SNOM with THz time domain spectroscopy (TDS). We describe the technical implementations that enabled this achievement and demonstrated its performance. We demonstrate hyperspectral THz nano-imaging in the frequency range spanning 0.5 THz to 1.8 THz by imaging charge carrier profiles of a heterogeneously doped Si semiconductor nanostructures. By fitting individual THz TDS s-SNOM spectra with a finite dipole theoretical model of s-SNOM and a Drude model for doped Si, we measure the local mobile charge carrier density. We also investigate doping modulated Si nanowires and quantify the carrier concentration using THz and mid-IR nanoscopy. The tip-sample near-field interaction for a Drude-type doped semiconductor sample is characterized by a step (respectively a weak resonance peak) in the amplitude spectrum near the plasma frequency and a peak in the phase spectrum. A spectral behavior that can be explained by a tip-induced plasmon resonance in the sample. Since the plasma frequency increases with carrier density, the amplitude step and phase peak shift to higher frequencies for higher carrier concentrations.