Traditionally, mathematicians have used results from the field of knot theory (the study of intertwined pieces of string in space) in order to study the field of contact topology (important in the study of 3- and 4-dimensional shapes). In this thesis, we do the converse: we use the famous Bennequin and slice-Bennequin inequalities (results from contact topology) in order to define new knot invariants. We then relate these new invariants to (strong-) quasipositivity of knots.