Over the past few years, ideas from symplectic geometry have had a major impact on low-dimensional topology. Some of the most impressive results stem from a set of invariants developed by Ozsvath and Szabo. Though defined using symplectic geometry, they turn out to be surprisingly powerful invariants of low-dimensional objects e.g. knots, and three- and four-manifolds. In this talk, I will survey these invariants and discuss how I have used them to prove results related to knot theory, complex curves, surgery theory in dimension three, and the theory of foliations and contact structures on three-manifolds.