Measurements of the interplay between the top quark and the Higgs at Tevatron and LHC

Given its large mass, the top quark plays an important role in the understanding of the mechanism for electroweak symmetry breaking (EWSB) in the Standard Model (SM). The recently observed new boson, consistent in many ways with the Higgs boson, could be the agent of EWSB. Studies of the production of this new particle in association with top-quark pairs will give important insight into the true nature of this particle. The current status of studies of $t\bar{t}$H production at the LHC and Tevatron are described herein, as well as one of the most important background channels, $t\bar{t}+b\bar{b}$ production. Further, the top quark plays an important role in exotic Higgs models; one such search is also described, looking for $t \rightarrow H^{\pm}b$.