Molecular ions have long been considered key intermediates in the evolution of molecular complexity in the interstellar medium. However, owing to their reactivity and transient nature, ions have historically proved challenging to study in terrestrial laboratory experiments. In turn, their detection and characterization in space is often contingent upon advances in the laboratory spectroscopic techniques used to measure their spectra. In this Review, we discuss the advances over the past 50 years in laboratory methodologies for producing molecular ions and probing their rotational, vibrational and electronic spectra. We largely focus this discussion around the widespread H3+ cation and the ionic products originating from its reaction with carbon atoms. Finally, we discuss the current frontiers in this research and the technical advances required to address the spectroscopic challenges that they represent.