Spectral lines from molecules and electron recombination at THz frequencies and below reveal the composition, motions, and physical properties of our Universe. We describe state-of-the-art research that uses these spectral lines in our Solar System, proto-planetary and stellar systems, the interstellar medium of the Milky Way, galaxies and active galactic nuclei in the nearby Universe, and throughout cosmic time. Astronomy research is entering a new paradigm, in which wideband instrumentation is enabling multiple species and transitions to be observed simultaneously, changing what is accessible to investigate with a single observation and fundamentally how observations are analyzed, including in distant galaxies for which the observed frequency of the line differs substantially from its rest frequency. The majority of the research described would not be possible using only the frequency ranges currently allocated to the Radio Astronomy Service. It is imperative to maintain the current protections and expand allocations below 100 GHz.

Faraday complexity describes whether a spectropolarimetric observation has simple or complex magnetic structure. Quickly determining the Faraday complexity of a spectropolarimetric observation is important for processing large, polarised radio surveys. Finding simple sources lets us build rotation measure grids, and finding complex sources lets us follow these sources up with slower analysis techniques or further observations. We introduce five features that can be used to train simple, interpretable machine learning classifiers for estimating Faraday complexity. We train logistic regression and extreme gradient boosted tree classifiers on simulated polarised spectra using our features, analyse their behaviour, and demonstrate our features are effective for both simulated and real data. This is the first application of machine learning methods to real spectropolarimetry data. With 95% accuracy on simulated ASKAP data and 90% accuracy on simulated ATCA data, our method performs comparably to state-of-the-art convolutional neural networks while being simpler and easier to interpret. Logistic regression trained with our features behaves sensibly on real data and its outputs are useful for sorting polarised sources by apparent Faraday complexity.