Because of their rich internal structure, trapped molecules offer great potential for precision spectroscopy experiments, including searches for time-variation of fundamental constants, parity violation studies, and searches for fundamental electric dipole moments. Unfortunately, precision of the best molecular spectroscopy is currently orders of magnitude behind atomic spectroscopy, owing primarily to challenges in molecular state preparation. Our group at Northwestern University is addressing this challenge by working with species having semi-closed electronic cycling transitions, so that optical pumping into the ground state can be achieved by spectrally filtering a single broadband laser. We have recently shown this technique to quickly and efficiently cool trapped AlH+ ions to their ground rotational state. Although we currently use a destructive two-photon state readout technique, these semi-cycling species are also promising candidates for single-molecule fluorescence detection. Beyond precision spectroscopy, molecular ion state preparation and nondestructive readout could be useful for quantum information processing, coherent molecular control, and ultracold chemistry applications.