Avian influenza viruses can cause severe disease when they spill over into mammalian and human hosts. H5N1 clade 2.3.4.4b has spread globally since 2021, decimating avian species, and has spilled over into mammalian species, causing sporadic infections and fatal outbreaks in sea lions, cats, mink and dairy cattle. Increased human cases of H5N1 are fuelling concern that H5N1 could soon adapt to become a new pandemic virus. Adaptive mutations have emerged following spillover, which support H5N1 outbreaks in mammalian populations and include changes to the PB2 such as E627K, D701N, M631L and T271A. Further changes to haemagglutinin, altering binding preference to human-like α2,6 sialic acid receptors have yet to be seen. Here, we review the adaptations that have emerged in mammals throughout the 2.3.4.4b outbreak and the molecular mechanisms behind these mutations to assess the pandemic risk of this virus.