Genetic improvement through breeding is one of the key approaches to increasing biomass supply. This paper documents the breeding progress to date for four perennial biomass crops (PBCs) that have high output-input energy ratios: namely Panicum virgatum (switchgrass), species of the genera Miscanthus (miscanthus), Salix (willow) and Populus (poplar). For each crop, we report on the size of germplasm collections, the efforts to date to phenotype and genotype, the diversity available for breeding and on the scale of breeding work as indicated by number of attempted crosses. We also report on the development of faster and more precise breeding using molecular breeding techniques. Poplar is the model tree for genetic studies and is furthest ahead in terms of biological knowledge and genetic resources. Linkage maps, transgenesis and genome editing methods are now being used in commercially focused poplar breeding. These are in development in switchgrass, miscanthus and willow generating large genetic and phenotypic data sets requiring concomitant efforts in informatics to create summaries that can be accessed and used by practical breeders. Cultivars of switchgrass and miscanthus can be seed-based synthetic populations, semihybrids or clones. Willow and poplar cultivars are commercially deployed as clones. At local and regional level, the most advanced cultivars in each crop are at technology readiness levels which could be scaled to planting rates of thousands of hectares per year in about 5 years with existing commercial developers. Investment in further development of better cultivars is subject to current market failure and the long breeding cycles. We conclude that sustained public investment in breeding plays a key role in delivering future mass-scale deployment of PBCs.