Terahertz time-domain measurements using air as the emission and detection medium are shown to enable broadband spectroscopy with continuous coverage of the entire terahertz band, from 0.1 to over 10 THz. It is shown that the unique properties of using a gaseous medium allow for excellent phase matching without interruptions from crystalline phonon modes or antenna resonant structures from conventional solid state emitters and sensors, allowing the full bandwidth of the laser pulse to be used. It is also shown that the limiting factor on the system bandwidth is the temporal profile of the probe pulse used for detection, and how modification of this profile can further enhance the detection bandwidth.