This chapter summarizes the trends in terahertz measurements on the surface of rigid and flexible substrates. It focuses on research incorporating fast photoconductive switches to generate and detect on-chip THz pulses using a femtosecond laser. The chapter aims to review progress toward the study of picosecond dynamics and THz spectroscopy of materials and liquids. We emphasize general sub-diffraction techniques for THz spectroscopy, transmission line and waveguide design considerations, time-domain measurements for studies of material dynamics, and provide a survey of recent research on the THz spectroscopy of materials and liquids on-chip. We conclude with an outlook on the field and highlight promising new directions. This chapter is meant to be an introduction and a general guide to this emerging field for new researchers interested in on-chip THz studies.