Large language models (LLMs), by virtue of their capacity to model complex semantic relationships and long-range contextual dependencies, have driven a paradigm shift in natural language processing research. Inspired by this progress, researchers have begun treating DNA sequences as biological symbol sequences with intrinsic contextual structure, giving rise to DNA language models tailored for genomic sequences. As livestock and poultry genomics enters a critical inflection point toward sequence-driven AI-assisted breeding, a systematic review of the theoretical foundations, application scenarios, and adaptation strategies of DNA language models in this domain is both timely and necessary, and may serve as a reference for building DNA language model frameworks oriented toward breeding tasks. This review first outlines the linguistic properties of DNA sequences, tokenization strategies, model architectures, training objectives, and fine-tuning paradigms. It then surveys downstream tasks including regulatory element identification, chromatin feature prediction, DNA modification prediction, variant effect assessment, and gene structure analysis, and compares representative models such as Basenji, DNABERT, Nucleotide Transformer, HyenaDNA, Evo 2, and AlphaGenome. The applicability and limitations of existing evaluation benchmarks in the context of livestock and poultry breeding are further discussed. Finally, drawing on the data characteristics and application requirements of livestock genetic improvement, this review analyzes the potential value of DNA language models in livestock and poultry breeding, proposes a tiered development roadmap suited to breeding-specific scenarios, and provides a technical reference for how DNA language models may advance livestock and poultry breeding research.