This thesis is organized into two independent parts. In the first part, we study the prospects for constraining the Higgs boson's couplings to up and down quarks using kinematic distributions in Higgs production at the CERN Large Hadron Collider. With 3000 inverse femtobarns of data in the four-lepton decay channel, we find that the Higgs pT distribution can be used to constrain these couplings with precision competitive to other proposed techniques. In the second part of the thesis, we perform the standard thermal relic abundance calculation for a generic WIMP for three different forms of the self-annihilation cross section. In particular, we consider s-wave annihilation, p-wave annihilation and resonant annihilation through a Higgs pole. We apply a numerical integration technique from the mathematical literature that does not appear to be well-known, but is particularly suited to this problem.