The recent advancements in far-infrared (far-IR) astronomy brought about by the Herschel, SOFIA, and ALMA observatories have led to technological advancements in millimeterwave and submillimeterwave laboratory spectroscopy that is used to support molecular observations. This review gives an overview of rotational spectroscopy and its relationship with observational astronomy, as well as an overview of laboratory spectroscopic techniques focusing on both historical approaches and new advancements. Additional topics discussed include production and detection techniques for unstable molecular species of astrochemical interest, data analysis approaches that address spectral complexity and line confusion, and the current state of and limitations to spectral line databases. Potential areas for new developments in this field are also reviewed. To advance the field, the following challenges must be addressed: Data acquisition speed, spectral sensitivity, and analysis approaches for complex mixtures and broadband spectra are the greatest limitations—and hold the greatest promise for advancement—in this field of research. Full science return from far-IR observatories cannot be realized until laboratory spectroscopy catches up with the data rate for observations. New techniques building on those used in the microwave and IR regimes are required to fill the terahertz gap.