Abstract: We give a complete classification of tight contact structures on every surgery along torus knots, which provides the first such classification on an infinite family of non-trivial knots and makes progress on the project of understanding tight contact structures on Seifert fibered spaces. The main tools are the classification of non-loose torus knots, bordered contact invariants, and non-thickenable tori in knot complements. In this talk, we will discuss the role played by recently developed connections between Heegaard Floer invariants and contact geometry in the classification.