The Vietoris-Rips complex of a metric space is the simplicial complex whose faces are the subsets of points with mutual distance smaller than a given threshold. We are interested in Vietoris-Rips complexes of hypercube graphs equipped with the Hamming distance. After reviewing known results about their homotopy type, I will describe a method for studying the homology of these complexes as a representation of the automorphism group of the hypercube. This is ongoing work with Jonathan Montaño and Zoe Wellner.