While the UK is the fourth largest aquaculture producer in Europe by volume, it is the second largest by value with an annual first sale value of around £1 billion. Over 90% of this value is from Atlantic salmon farmed in Scotland, but other finfish and shellfish aquaculture species are important to several UK regions. In this review, we describe the state of the art in UK aquaculture breeding and stock supply, and how innovation in genetics technologies can help achieve the Scottish Government's ambitious target of doubling its aquaculture industry by 2030. Particular attention is given to the four most important UK aquaculture species: Atlantic salmon, rainbow trout, blue mussel and Pacific oyster, and we contrast the highly variable level of selective breeding and genomics technologies used in these sectors. A major factor in the success of Atlantic salmon farming has been large-scale investment in modern breeding programmes, including family selection programmes and genomic selection. This has proven cost-effective at scale, leading to improved production efficiency and reduction of some infectious diseases. We discuss the feasibility of applying similar technologies to the UK shellfish sectors, to ensure consistent and robust spat supply and begin trait selection. Furthermore, we discuss species-specific application of modern breeding technologies in a global context, and the future potential of genomics and genome editing technologies to improve commercially desirable traits. Increased adoption of modern breeding technologies will assist UK aquaculture industries to meet the challenges for sustainable expansion, and remain competitive in a global market.