This talk will focus on the homology concordance group of knots in integer homology 3-spheres bounding integer homology 4-spheres. Using knot Floer homology, we will construct integer-valued homomorphisms from the homology concordance group. This leads to the existence of an infinite rank summand of the quotient group of the homology concordance group modded out by knots in the 3-sphere. This is joint work with Irving Dai, Jennifer Hom, and Matthew Stoffregen.