Biological materials are self-assembled with near-atomic precision in living cells, whereas synthetic 3D structures generally lack such precision and controllability. Recently, DNA nanotechnology, especially DNA origami technology, has been useful in the bottom-up fabrication of well-defined nanostructures ranging from tens of nanometres to sub-micrometres. In this Primer, we summarize the methodologies of DNA origami technology, including origami design, synthesis, functionalization and characterization. We highlight applications of origami structures in nanofabrication, nanophotonics and nanoelectronics, catalysis, computation, molecular machines, bioimaging, drug delivery and biophysics. We identify challenges for the field, including size limits, stability issues and the scale of production, and discuss their possible solutions. We further provide an outlook on next-generation DNA origami techniques that will allow in vivo synthesis and multiscale manufacturing.