The branching fraction for the decays of gluinos to third generation quarks is expected to be enhanced in classes of supersymmetric models where either third generation squarks are lighter than other squarks, or in mixed-higgsino dark matter models constructed to be in concordance with the measured density of cold dark matter. In such scenarios, gluino production events at the CERN Large Hadron Collider should be rich in top and bottom quark jets. Requiring b-jets in addition to missing transverse energy should, therefore, enhance the supersymmetry signal relative to Standard Model backgrounds from V + jet, VV and QCD backgrounds (V=W, Z). We quantify the increase in the supersymmetry reach of the LHC from b-tagging in a variety of well-motivated models of supersymmetry. We also explore ``top-tagging at the LHC. We find that while the efficiency for this turns out to be too low to give an increase in reach beyond that obtained via b-tagging, top-tagging can indeed provide a confirmatory signal if gluinos are not too heavy. Finally, we explore the prospects for detecting the direct production of third generation squarks in models with an inverted squark mass hierarchy. This is signalled by b-jets + missing transverse energy events harder than in the Standard Model, but softer than those from the production of gluinos and heavier squarks. We find that while these events can be readily separated from SM background (for third generation squark masses ~300-500 GeV), the contamination from the much heavier gluinos and squarks remains formidable if these are also accessible.