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Recent technological advances in next-generation sequencing (NGS) technologies have dramatically reduced the cost of DNA sequencing, allowing species with large and complex genomes to be sequenced. Although bread wheat (Triticum aestivum L.) is one of the world's most important food crops, efficient exploitation of molecular marker-assisted breeding approaches has lagged behind that achieved in other crop species, due to its large polyploid genome. However, an international public-private effort spanning 9 years reported over 65% draft genome of bread wheat in 2014, and finally, after more than a decade culminated in the release of a gold-standard, fully annotated reference wheat-genome assembly in 2018. Shortly thereafter, in 2020, the genome of assemblies of additional 15 global wheat accessions was released. As a result, wheat has now entered into the pan-genomic era, where basic resources can be efficiently exploited. Wheat genotyping with a few hundred markers has been replaced by genotyping arrays, capable of characterizing hundreds of wheat lines, using thousands of markers, providing fast, relatively inexpensive, and reliable data for exploitation in wheat breeding. These advances have opened up new opportunities for marker-assisted selection (MAS) and genomic selection (GS) in wheat. Herein, we review the advances and perspectives in wheat genetics and genomics, with a focus on key traits, including grain yield, yield-related traits, end-use quality, and resistance to biotic and abiotic stresses. We also focus on reported candidate genes cloned and linked to traits of interest. Furthermore, we report on the improvement in the aforementioned quantitative traits, through the use of (i) clustered regularly interspaced short-palindromic repeats/CRISPR-associated protein 9 (CRISPR/Cas9)-mediated gene-editing and (ii) positional cloning methods, and of genomic selection. Finally, we examine the utilization of genomics for the next-generation wheat breeding, providing a practical example of using in silico bioinformatics tools that are based on the wheat reference-genome sequence., HB was funded by USDA-NIFA SBIRI and SBIRII. PH and SG were funded by project P18-RT-992 from Junta de Andalucía (Andalusian Regional Government), Spain (Co-funded by FEDER). JC was funded by BBSRC grant BB/P010741/1. MF is supported by the 2Blades Foundation and Grains Research and Development Corporation (project CSP1801-013RTX/9176010). VK is supported by the Ministry of Science and Higher Education of the Russian Federation (grant no. 075-15-2019-1881). GH was supported by funding of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2048/1—project ID 390686111 and grants 426557363 and 458717903, the European Regional Development Fund (Project ID ZS/2018/06/93171), and the Czech Science Foundation (CZ.02.1.01./0.0/0.0/16_019/0000827, SPP 813103381). BK thanks the Government of Norway (QZA-14/0005) for funding the initiative of “Adapting Agriculture to Climate Change: Collecting, Protecting and Preparing Crop Wild Relatives” (https://www.cwrdiversity.org/project/pre-breeding/).