MOTIVATION: Pangenomes provide novel insights for population and quantitative genetics, genomics and breeding not available from studying a single reference genome. Instead, a species is better represented by a pangenome or collection of genomes. Unfortunately, managing and using pangenomes for genomically diverse species is computationally and practically challenging. We developed a trellis graph representation anchored to the reference genome that represents most pangenomes well and can be used to impute complete genomes from low density sequence or variant data. RESULTS: The Practical Haplotype Graph (PHG) is a pangenome pipeline, database (PostGRES & SQLite), data model (Java, Kotlin or R) and Breeding API (BrAPI) web service. The PHG has already been able to accurately represent diversity in four major crops including maize, one of the most genomically diverse species, with up to 1000-fold data compression. Using simulated data, we show that, at even 0.1× coverage, with appropriate reads and sequence alignment, imputation results in extremely accurate haplotype reconstruction. The PHG is a platform and environment for the understanding and application of genomic diversity. AVAILABILITY AND IMPLEMENTATION: All resources listed here are freely available. The PHG Docker used to generate the simulation results is https://hub.docker.com/ as maizegenetics/phg:0.0.27. PHG source code is at https://bitbucket.org/bucklerlab/practicalhaplotypegraph/src/master/. The code used for the analysis of simulated data is at https://bitbucket.org/bucklerlab/phg-manuscript/src/master/. The PHG database of NAM parent haplotypes is in the CyVerse data store (https://de.cyverse.org/de/) and named/iplant/home/shared/panzea/panGenome/PHG_db_maize/phg_v5Assemblies_20200608.db. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.