Different mechanisms operate in various regions of the MSSM parameter space to bring the relic density of the lightest neutralino, χ~01χ~10 , assumed here to be the lightest SUSY particle (LSP) and thus the dark matter (DM) particle, into the range allowed by astrophysics and cosmology. These mechanisms include coannihilation with some nearly degenerate next-to-lightest supersymmetric particle such as the lighter stau τ~1τ~1 , stop t~1t~1 or chargino χ~±1χ~1± , resonant annihilation via direct-channel heavy Higgs bosons H / A, the light Higgs boson h or the Z boson, and enhanced annihilation via a larger Higgsino component of the LSP in the focus-point region. These mechanisms typically select lower-dimensional subspaces in MSSM scenarios such as the CMSSM, NUHM1, NUHM2, and pMSSM10. We analyze how future LHC and direct DM searches can complement each other in the exploration of the different DM mechanisms within these scenarios. We find that the τ~1τ~1 coannihilation regions of the CMSSM, NUHM1, NUHM2 can largely be explored at the LHC via searches for /ET/ET events and long-lived charged particles, whereas their H / A funnel, focus-point and χ~±1χ~1± coannihilation regions can largely be explored by the LZ and Darwin DM direct detection experiments. We find that the dominant DM mechanism in our pMSSM10 analysis is χ~±1χ~1± coannihilation: parts of its parameter space can be explored by the LHC, and a larger portion by future direct DM searches.