Nanopore analysis is an emerging technique that involves using a voltage to drive molecules through a nanoscale pore in a membrane between two electrolytes, and monitoring how the ionic current through the nanopore changes as single molecules pass through it. This approach allows charged polymers (including single-stranded DNA, double-stranded DNA and RNA) to be analysed with subnanometre resolution and without the need for labels or amplification. Recent advances suggest that nanopore-based sensors could be competitive with other third-generation DNA sequencing technologies, and may be able to rapidly and reliably sequence the human genome for under $1,000. In this article we review the use of nanopore technology in DNA sequencing, genetics and medical diagnostics.