Crop improvement by genome editing involves the targeted alteration of genes to improve plant traits, such as stress tolerance, disease resistance or nutritional content. Techniques for the targeted modification of genomes have evolved from generating random mutations to precise base substitutions, followed by insertions, substitutions and deletions of small DNA segments, and are finally starting to achieve precision manipulation of large DNA segments. Recent developments in base editing, prime editing and other CRISPR-associated systems have laid a solid technological foundation to enable plant base research and precise molecular breeding. In this Review, we systematically outline the technological principles underlying precise and targeted genome-modification methods. We also review methods for the delivery of genome-editing reagents in plants and outline emerging crop-breeding strategies based on targeted genome modification. Finally, we consider potential future developments in precise genome-editing technologies, delivery methods and crop-breeding approaches, as well as regulatory policies for genome-editing products.