A new genotype imputation method and web service are described, offering significant improvements in computational efficiency without sacrificing accuracy. The method reduces computational requirements by more than an order of magnitude compared to standard imputation tools. A web-based imputation service is also introduced, enabling access to new reference panels and improving user experience and productivity. Genotype imputation is a key component of genetic association studies, increasing power, facilitating meta-analysis, and aiding interpretation of signals. After study samples are genotyped on an array, imputation finds haplotype segments shared by study individuals and a reference panel of sequenced genomes. Imputation accurately assigns genotypes at untyped markers, improving genome coverage, facilitating comparison and combination of studies, increasing power to detect genetic association, and guiding fine-mapping. Imputation accuracy increases with the number of haplotypes in the reference panel, particularly for rare and low-frequency variants. Large reference panels, such as the Haplotype Reference Consortium (HRC) panel, extend accurate imputation to variants with frequencies of 0.1–0.5% or less. The HRC panel combines sequence data across >32,000 individuals from >20 medical sequencing studies and is cumbersome to access directly. The new algorithm for genotype imputation leverages local similarities between sequenced haplotypes to increase computational efficiency without loss of accuracy. A new web-based imputation service simplifies analysis, eliminates the need for cumbersome data access agreements, and allows users to focus on other essential tasks. The methods described provide an extremely efficient strategy for genotype imputation. Together, they ensure accurate imputation while reducing computational requirements and user time. Our implementation supports reference panels composed of hundreds of thousands of haplotypes and is freely available, enabling others to build on our work. The new algorithm, minimac3, outperforms existing tools in terms of computational efficiency and imputation accuracy. It is based on a 'state space reduction' of the hidden Markov models (HMMs) describing haplotype sharing. It exploits similarities among haplotypes in small genomic segments to reduce the effective number of states over which the HMM iterates. minimac3 consistently outperformed all alternatives in terms of computational efficiency and imputation accuracy. The new web-based imputation service is cloud-based, combining minimac3, the MapReduce paradigm, and a user-friendly interface. It allows users to access large reference panels and facilitates analysis steps. The server uses Apache Hadoop MapReduce for low-level tasks and the Cloudgene workflow system to drive the user interface. It automatically performs quality checks and provides feedback on progress, summary reports, email notifications, and download links for imputed data. The new methods enable researchers to rapidly impute large numbers of samples without becoming experts in imputation software and cluster job management. They also allow convenient access to large reference panels of sequenced individuals. The methods are scalable and efficient, enabling the use of large referenceA new genotype imputation method and web service are described, offering significant improvements in computational efficiency without sacrificing accuracy. The method reduces computational requirements by more than an order of magnitude compared to standard imputation tools. A web-based imputation service is also introduced, enabling access to new reference panels and improving user experience and productivity. Genotype imputation is a key component of genetic association studies, increasing power, facilitating meta-analysis, and aiding interpretation of signals. After study samples are genotyped on an array, imputation finds haplotype segments shared by study individuals and a reference panel of sequenced genomes. Imputation accurately assigns genotypes at untyped markers, improving genome coverage, facilitating comparison and combination of studies, increasing power to detect genetic association, and guiding fine-mapping. Imputation accuracy increases with the number of haplotypes in the reference panel, particularly for rare and low-frequency variants. Large reference panels, such as the Haplotype Reference Consortium (HRC) panel, extend accurate imputation to variants with frequencies of 0.1–0.5% or less. The HRC panel combines sequence data across >32,000 individuals from >20 medical sequencing studies and is cumbersome to access directly. The new algorithm for genotype imputation leverages local similarities between sequenced haplotypes to increase computational efficiency without loss of accuracy. A new web-based imputation service simplifies analysis, eliminates the need for cumbersome data access agreements, and allows users to focus on other essential tasks. The methods described provide an extremely efficient strategy for genotype imputation. Together, they ensure accurate imputation while reducing computational requirements and user time. Our implementation supports reference panels composed of hundreds of thousands of haplotypes and is freely available, enabling others to build on our work. The new algorithm, minimac3, outperforms existing tools in terms of computational efficiency and imputation accuracy. It is based on a 'state space reduction' of the hidden Markov models (HMMs) describing haplotype sharing. It exploits similarities among haplotypes in small genomic segments to reduce the effective number of states over which the HMM iterates. minimac3 consistently outperformed all alternatives in terms of computational efficiency and imputation accuracy. The new web-based imputation service is cloud-based, combining minimac3, the MapReduce paradigm, and a user-friendly interface. It allows users to access large reference panels and facilitates analysis steps. The server uses Apache Hadoop MapReduce for low-level tasks and the Cloudgene workflow system to drive the user interface. It automatically performs quality checks and provides feedback on progress, summary reports, email notifications, and download links for imputed data. The new methods enable researchers to rapidly impute large numbers of samples without becoming experts in imputation software and cluster job management. They also allow convenient access to large reference panels of sequenced individuals. The methods are scalable and efficient, enabling the use of large reference