Terahertz (THz) radiation opens transformational fundamental science possibilities in physics, chemistry, biology, and neuroscience, as well as various novel applications in communication, defense, remote probing, and non-invasive imaging. The THz spectral region (~0.1 THz to ~20 THz) spans the energy scales of many fundamental excitations in solids that include lattice vibrations, superconductivity, electronic spin excitations, and plasmon polaritons to name a few. Our research focuses on real-space nano-imaging at THz frequencies and investigation of spin plasmon waves in topological insulators and nanospectroscopic investigation of semiconductor dislocations, interfaces, defects, and carrier density variations as function of depth in semiconductors.