This dissertation presents the Terahertz spectroscopy of several systems ranging from proteins to nanostructures. First, Terahertz Time-Domain Spectroscopy is introduced as a unique and powerful technique for studying physical processes that occur at Terahertz frequencies or on picosecond timescales. A detailed analysis of the design, construction, and performance of different types of Terahertz Time-Domain Spectrometers is presented. Next, discussion of the Terahertz frequency response of Bovine Serum Albumin protein and novel integrated photonic components measured using these spectrometers is discussed. In the penultimate and final chapters of this dissertation, the study of the ultrafast carrier dynamics in optically excited epitaxial graphene and germanium nanowires, respectively, using multi-color Optical-Pump Terahertz-Probe Spectroscopy is presented.