Laser-driven terahertz (THz) pulses are popular because of their numerous applications, e.g., in security screening, medical imaging, time-domain spectroscopy and remote detection. At non-relativistic intensity, two-color optical pulses can create air plasmas that supply suitable emitters free of any damage, which are nowadays employed for an efficient molecular spectroscopy. Electrons are tunnel ionized by the asymmetric light field and the resulting photocurrent generates an ultrabroadband terahertz radiation with field strength > 0.1GV/m. At relativistic intensities, plasma waves trigger strong longitudinal fields used in laser wake-field particle acceleration. THz field strengths approaching the TV/m level can then be delivered by immersing the plasma in strong external magnetic fields. This talk will review the different physical mechanisms involved in terahertz emissions by laser-gas interactions at various intensities. Recent results on air-plasma based THz spectroscopy of solid materials will be presented in the context of the project ALTESSE. The last part of the talk will discuss new perspectives in the production of ultra-intense terahertz pulses from relativistic plasmas.