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It is well known that magnetic impurity model helps us to understand the low-temperature properties of magnetic-doped materials in the dilute limit.Those properties include the ordering of impurities, the temperature dependent of the spin susceptibility and the conductivity, etc.Magnetic impurity problem with host being normal metal has been extensively studied over the decades, e.g., the famous Kondo problem.However, for recent discovered materials such as graphene and topological insulator, the behaviors of magnetic impurities are far from clear.In the first part of this talk, I will introduce physical motivations and model Hamiltonians.Then, I will briefly talk about a useful quantum Monte Carlo simulation algorithm, the Hirsch-Fye algorithm, used for impurity problems, and its new development in spin-orbit coupled systems.Finally, I will present our recent works on (1) the magnetic impurity problems in graphene;(2) the spin-spin interaction in the bulk of topological insulators;and (3) the Kondo temperature of the 2-dimensional electron gas with Rashba spin-orbit coupling.Quantities such as local moment formation, spin-spin correlation, and universal curves of spin susceptibility will be discussed.