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Abstract Motivation Current methods for genotype imputation and phasing exploit the volume of data in haplotype reference panels and rely on hidden Markov models (HMMs). Existing programs all have essentially the same imputation accuracy, are computationally intensive and generally require prephasing the typed markers. Results We introduce a novel data-mining method for genotype imputation and phasing that substitutes highly efficient linear algebra routines for HMM calculations. This strategy, embodied in our Julia program MendelImpute.jl, avoids explicit assumptions about recombination and population structure while delivering similar prediction accuracy, better memory usage and an order of magnitude or better run-times compared to the fastest competing method. MendelImpute operates on both dosage data and unphased genotype data and simultaneously imputes missing genotypes and phase at both the typed and untyped SNPs (single nucleotide polymorphisms). Finally, MendelImpute naturally extends to global and local ancestry estimation and lends itself to new strategies for data compression and hence faster data transport and sharing. Availability and implementation Software, documentation and scripts to reproduce our results are available from https://github.com/OpenMendel/MendelImpute.jl. Supplementary information Supplementary data are available at Bioinformatics online.