At the basis of hierarchical theories of galaxy formation are mergers between galaxies, which are believed to trigger intense star formation and supermassive black hole accretion. Post-starburst E+A galaxies are believed to be systems in a rapid transition between major merger starbursts and quiescent ellipticals. Although this is a common stage in galaxy evolution, it is still not clear what causes the sudden quenching of star formation. In this talk, I will review recent observational efforts to constrain the molecular gas and star formation properties in such systems, which revealed many surprises, including (i) large molecular gas reservoirs in apparently-quenched galaxies, (ii) significant differences between different star formation rate tracers, and more. I will discuss how these observations paint a more complex picture of these transitioning sources, and the broader implications of these results to high-redshift galaxies in the JWST+ALMA era.