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We review variational and quantum Monte Carlo approaches based on (extended)Lang-Firsov transformations of the Hamiltonian. Derivations for one, two andmany electrons are given, and results for the Holstein polaron, theHolstein-Hubbard bipolaron, and the spinless Holstein model at finite carrierdensities are presented.Comment: 40 pages, 15 figures, to be published in Polarons in Advanced  Materials, Ed. A. S. Alexandrov (Canopus/Springer Publishing, Bristol)  (2007); V2: typo in authors list correcte

Lang-Firsov Approaches to Polaron Physics: From Variational Methods to Unbiased Quantum Monte Carlo Simulations