(22 votes from 15 institutions)
The detailed spatial structure of stellar populations with different chemical abundances in the Milky Way's disk contains a wealth of information on Galactic growth and evolution over cosmic time. We use data on 14,699 red-clump stars from the spectroscopic APOGEE survey, covering 4 <~ R <~ 15 kpc, to determine the spatial structure of mono-abundance populations (MAPs)---stars in narrow bins in [a/Fe] and [Fe/H]---accounting for the effects of the APOGEE selection function and the spatially-variable dust obscuration. We determine that all MAPs with enhanced [a/Fe] are centrally concentrated and are well-described as exponentials with a scale length of 2.2+/-0.2 kpc over the whole radial range of the disk. We discover that the radial surface-density profiles of low-[a/Fe] MAPs are complex: they do not monotonically decrease outwards, but rather display a peak radius ranging from ~5 kpc to ~13 kpc. The radial coverage of the data allows us to measure radial trends in each MAP's thickness. While high-[a/Fe] MAPs have constant scale heights everywhere, low-[a/Fe] MAPs flare outward, with an exponential flaring profile with a scale length of 8.5+/-0.7 kpc. We confirm, now with high-precision abundances, previous results that each MAP contains only a single vertical scale height. We also confirm that low-[Fe/H], low-[a/Fe] and high-[Fe/H], high-[a/Fe] MAPs have intermediate scale heights that smoothly bridge the traditional thin- and thick-disk divide. That the high-[a/Fe], thick disk components do not flare is strong evidence against their thickness being caused by radial migration or satellite heating. The correspondence between the radial structure and chemical-enrichment age of stellar populations is clear confirmation of the inside-out growth of galactic disks. The details of these relations will constrain the variety of physical conditions under which stars form throughout the MW disk.