This talk will be about knots that are transversal to the standard contact structure in ${\mathbb{R}}^3$. I'll define this contact structure and describe some of its geometric properties. A transversal knot type (where this means that admissible isotopies are through transversal knots) is transversally simple if it is determined by its topological knot type ${\mathcal K}$ and its Bennequin number. I'll discuss recent work with Nancy Wrinkle and (briefly) related work with Bill Menasco. The main theorem in the paper with Nancy aserts that any ${\mathcal TK}$ whose associated topological knot type ${\mathcal K}$ satisfies a condition that we call exchange reducibility is transversally simple.