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We will introduce the Stochastic Series Expansion (SSE) Quantum Monte Carlo method which is very useful in the study of quantum spin systems and some Hubbard models.The method is used to study the quasi-two-dimensional Heisenberg antiferromagnets and square-lattice Heisenberg antiferromagnets with disorder.For the quasi-two-dimensional Heisenberg antiferromagnets, we calculate the Neel temperature T_N of weakly coupled S=1/2 Heisenberg antiferromagnetic layers consisting of coupled ladders.This system can be tuned to different two-dimensional scaling regimes for T > T_N.We find some interesting universal scaling functions for the quasi-two-dimensional Heisenberg antiferromagnets.Then we use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition in square-lattice S=1/2 Heisenberg antiferromagnets with intra-and inter-dimer couplings J and J.The system undergoes a quantum phase transition the by tuning the ratio g=J/J.The dimers are either randomly distributed, or come in parallel pairs with horizontal or vertical orientation.In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >=1.We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu =0.71).In the end, we will talk about some recent work on Bose glass phase in square lattice with disordered couplings.