I read (or skimmed, really) some classic papers on the star-formation history of the Milky Way, in preparation for re-asking this question with APOGEE data this summer. Papers I skimmed included Prantzos & Silk, which infers the SFH from (mainly) abundance distributions and Gizis, Reid, and Hawley, which infers it from M-dwarf chromospheric activity. I also wrote myself a list of all the possible ways one might infer the SFH. I realized that not all of the ways I can think of have actually been executed. So now I have a whole set of projects to pitch!