The vast majority of prenatal genetic testing requires invasive sampling. However, this poses a risk to the fetus, so one must make a decision that weighs the desire for genetic information against the risk of an adverse outcome due to hazards of the testing process. These issues are not required to be coupled, and it would be desirable to discover genetic information about the fetus without incurring a health risk. Here we demonstrate that it is possible to non-invasively sequence the entire prenatal genome. Our results show that molecular counting of parental haplotypes in maternal plasma by shotgun sequencing of maternal plasma DNA allows the inherited fetal genome to be deciphered non-invasively. We also applied the counting principle directly to each allele in the fetal exome by performing exome capture on maternal plasma DNA before shotgun sequencing. This approach enables non-invasive exome screening of clinically relevant and deleterious alleles that were paternally inherited or had arisen as de novo germline mutations, and complements the haplotype counting approach to provide a comprehensive view of the fetal genome. Non-invasive determination of the fetal genome may ultimately facilitate the diagnosis of all inherited and de novo genetic disease.