We propose two new analysis strategies for studying charm and beauty quarks at colliders. The first strategy is aimed at testing the kinematics of heavy-flavor quarks within an identified jet. Here, we use the SoftDrop jet-declustering algorithm to identify two subjets within a large-radius jet, using subjet flavor tagging to test the heavy-quark splitting functions of QCD. For subjets containing a J=ψ or ϒ, this declustering technique can also help probe the mechanism for quarkonium production. The second strategy is aimed at isolating heavy-flavor production from gluon splitting. Here, we introduce a new FlavorCone algorithm, which smoothly interpolates from well-separated heavy-quark jets to the gluon-splitting regime where jets overlap. Because of its excellent ability to identify charm and beauty hadrons, the LHCb detector is ideally suited to pursue these strategies, though similar measurements should also be possible at ATLAS and CMS. Together, these SoftDrop and FlavorCone studies should clarify a number of aspects of heavyflavor physics at colliders, and provide crucial information needed to improve heavy-flavor modeling in parton-shower generators.