Collisions at the Large Hadron Collider (LHC) are dominated by jets, collimated sprays of particles that arise from quantum chromodynamics (QCD) at high energies. With the remarkable performance of the ATLAS and CMS detectors, jets can now be characterized not just by their overall direction and energy but also by their substructure. In this talk, I highlight the increasingly important role that jet substructure is playing in searches for dark matter and other new physics at the LHC, especially when exploring extreme kinematic regimes involving large Lorentz boosts. I also explain how innovative theoretical studies of jet substructure have taught us surprising lessons about QCD, revealing new probes of hot dense matter and universal features of gauge theories.