A slice knot is a knot in a three-sphere that is the boundary of a disk in a four-ball; we also say that such a knot is concordant to the unknot. One would like a nice invariant that distinguishes slice knots; however, no such invariant has been found. I will present an overview of the work that has been done in this direction, beginning with the concept of algebraic sliceness, and covering the invariants of Casson and Gordon, work done using Casson-Gordon and related invariants to understand the knot concordance group, especially its torsion elements, and some recent work to extend Casson-Gordon invariants.