We introduce Aquila, a new approach to variant discovery in personal genomes, which is critical for uncovering the genetic contributions to health and disease. Aquila uses a reference sequence and linked-read data to generate a high quality diploid genome assembly, from which it then comprehensively detects and phases personal genetic variation. The contigs of the assemblies from our libraries cover >95% of the human reference genome, with over 98% of that in a diploid state. Thus, the assemblies support detection and accurate genotyping of the most prevalent types of human genetic variation, including single nucleotide polymorphisms (SNPs), small insertions and deletions (small indels), and structural variants (SVs), in all but the most difficult regions. All heterozygous variants are phased in blocks that can approach arm-level length. The final output of Aquila is a diploid and phased personal genome sequence, and a phased Variant Call Format (VCF) file that also contains homozygous and a few unphased heterozygous variants. Aquila represents a cost-effective approach that can be applied to cohorts for variation discovery or association studies, or to single individuals with rare phenotypes that could be caused by SVs or compound heterozygosity.