In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration of the classical knot concordance group. The filtration is defined in terms of gropes or Whitney towers and is connected to the classification of topological 4-manifolds. We will discuss some joint work with Tim Cochran and Shelly Harvey that establishes explicit families of knots that generate infinite rank subgroups of each filtration quotient.