Second-generation sequencing (SGS) has advanced the study of crop genomes and has provided insights into diversity and evolution. However, repetitive DNA sequences in crops often lead to incomplete or erroneous assemblies because SGS reads are too short to fully resolve these repeats. To overcome some of these challenges, long-read sequencing and optical mapping have been developed to produce high-quality assemblies for complex genomes. Previously, high error rates, low throughput, and high costs have limited the adoption of long-read sequencing and optical mapping. However, with recent improvements and the development of novel algorithms, the application of these technologies is increasing. We review the development of long-read sequencing and optical mapping, and assess their application in crop genomics for breeding improved crops. Short-read second-generation DNA sequencing has revolutionised our understanding of biology but suffers from significant limitations of scale.Long-read sequencing and optical mapping promise to deliver long-range genomic information, but their adoption has been hampered by low throughput and relatively high error rates.Recent improvements in these long-range technologies have overcome these issues, and open broad applications for genome assembly and the analysis of genome structural variation.These advances will facilitate our understanding of genome structural diversity and heritable agronomic traits, accelerating the development of improved crop varieties to feed the expanding human population.