Terahertz (THz) spectroscopy is a well-established technique which allows for measuring the complex-valued dielectric properties of materials, specifically semiconductors, in the THz range. As THz photons have a low energy, typically comparable to intraband transitions, they are ideal probes of important phenomena such as the momentum relaxation of charge carriers and optical phonons. Because of the intrinsic phase-matching limitations imposed by the materials employed in conventional THz emitters and detectors, most femtosecond-laser based THz spectrometers can only cover a narrow spectral range, typically 0.1-3 THz. However, by employing the same laser source as conventional THz spectrometers, an air-photonics based THz spectrometer can access a much broader spectral range, extending beyond 30 THz. As air is virtually non-dispersive, the optical-THz phase-matching condition is automatically met. As a result, intense, sub-50-fs electromagnetic transients can be achieved with THz air photonics. The enhanced characteristics in terms of time-resolution, bandwidth, and field strength offer unique opportunities for THz spectroscopy, such as monitoring the dynamics of the charge carriers on the timescale of the carrier-lattice interaction. In this thesis, we explore the capabilities of THz air photonics by performing steady-state ultra-broadband THz spectroscopy of some common polymers, and transient ultra-broadband THz spectroscopy of, respectively, solution processed methylammonium lead iodide perovskite films and undoped gallium arsenide. In addition, we present explicit guidelines for ultra-broadband transient THz spectroscopy, including a novel method for self-referenced signal acquisition minimizing the phase error, and a numerically-accurate approach to the transient reflectance data analysis.