The Cdc45/Mcm2-7/GINS (CMG) helicase separates DNA strands during replication in eukaryotes. How the CMG is assembled and engages DNA substrates remains unclear. Using electron microscopy, we have determined the structure of the CMG in the presence of ATPγS and a DNA duplex bearing a 3′ single-stranded tail. The structure shows that the MCM subunits of the CMG bind preferentially to single-stranded DNA, establishes the polarity by which DNA enters into the Mcm2-7 pore, and explains how Cdc45 helps prevent DNA from dissociating from the helicase. The Mcm2-7 subcomplex forms a cracked-ring, right-handed spiral when DNA and nucleotide are bound, revealing unexpected congruencies between the CMG and both bacterial DnaB helicases and the AAA+ motor of the eukaryotic proteasome. The existence of a subpopulation of dimeric CMGs establishes the subunit register of Mcm2-7 double hexamers and together with the spiral form highlights how Mcm2-7 transitions through different conformational and assembly states as it matures into a functional helicase. DOI: http://dx.doi.org/10.7554/eLife.03273.001