Haplotyping of human chromosomes is a prerequisite for cataloguing the full repertoire of genetic variation. We present a microfluidics-based, linked-read sequencing technology that can phase and haplotype germline and cancer genomes using nanograms of input DNA. This high-throughput platform prepares barcoded libraries for short-read sequencing and computationally reconstructs long-range haplotype and structural variant information. We generate haplotype blocks in a nuclear trio that are concordant with expected inheritance patterns and phase a set of structural variants. We also resolve the structure of the EML4-ALK gene fusion in the NCI-H2228 cancer cell line using phased exome sequencing. Finally, we assign genetic aberrations to specific megabase-scale haplotypes generated from whole-genome sequencing of a primary colorectal adenocarcinoma. This approach resolves haplotype information using up to 100 times less genomic DNA than some methods and enables the accurate detection of structural variants.