T cells initiate and regulate adaptive immune responses that can clear infections. To do this, they use their T cell receptors (TCRs) to continually scan the surfaces of other cells for cognate peptide antigens presented on major histocompatibility complexes (pMHCs). Experimental work has established that as few 1-10 pMHCs are sufficient to activate T cells. This sensitivity is remarkable in light of a number of factors, including the observation that the TCR and pMHC are short molecules relative to highly abundant long surface molecules, such as CD45, that can hinder initial binding, and moreover, the TCR/pMHC interaction is of weak affinity with solution lifetimes of approximately 1 second. Here, we review experimental and mathematical work that has contributed to uncovering molecular mechanisms of T cell sensitivity. We organize the mechanisms by where they act in the pathway to activate T cells, namely mechanisms that (a) promote TCR/pMHC binding, (b) induce rapid TCR signaling, and (c) amplify TCR signaling. We discuss work showing that high sensitivity reduces antigen specificity unless molecular feedbacks are invoked. We conclude by summarizing a number of open questions.