Pangenome graphs are revolutionising evolutionary and population genomics by moving beyond linear reference genomes to represent the full spectrum of sequence diversity within and across species. This review traces the field’s progression from reference-augmented graphs to assembly-based, alignment-first approaches that capture complex structural variation with reduced bias. We examine key strategies for graph construction, genotyping and implementing graph-aware tools in functional genomics, including transcriptomics and epigenomics. While much of the work to date has focused on humans, diverse and structurally complex plant genomes pose unique challenges that require further methodological innovation. Key bottlenecks – including visualisation, scalability and integration with multi-omic data – persist. By outlining trade-offs among current tools and emphasising the need for rigorous evaluation frameworks, we argue that progress will depend on community-driven efforts to unify graph construction, genotyping and interpretation. Despite technical hurdles, pangenome graphs offer a powerful foundation for more inclusive evolutionary and population genomics.