Genomics is transforming medicine and our understanding of life in fundamental ways. Genomics data, however, is far outpacing Moore’s Law. Third-generation sequencing technologies produce 100× longer reads than second generation technologies and reveal a much broader mutation spectrum of disease and evolution. However, these technologies incur prohibitively high computational costs. Over 1,300 CPU hours are required for reference-guided assembly of the human genome, and over 15,600 CPU hours are required for de novo assembly. This paper describes “Darwin” — a co-processor for genomic sequence alignment that, without sacrificing sensitivity, provides up to 15,000× speedup over the state-of-the-art software for reference-guided assembly of third-generation reads. Darwin achieves this speedup through hardware/algorithm co-design, trading more easily accelerated alignment for less memory-intensive filtering, and by optimizing the memory system for filtering. Darwin combines a hardware-accelerated version of D-SOFT, a novel filtering algorithm, with a hardware-accelerated version of GACT, a novel alignment algorithm. GACT generates near-optimal alignments of arbitrarily long genomic sequences using constant memory for the compute-intensive step. Darwin is adaptable, with tunable speed and sensitivity to match emerging sequencing technologies and to meet the requirements of genomic applications beyond read assembly.