One very important object of study in low-dimensional topology is the homology cobordism group. The structure of this group is largely unknown, although it is abelian and it is known that it is very large (it contains an infinite rank summand). In this talk, we will review the basics of this group, as well as more recent developments. We will end with some results which can be derived from Hendricks and Manolescu’s theory of involutive Heegaard Floer homology, focusing on a formula for Dehn surgery due to Hendricks, Hom, Stoffregen and myself.