A method based on trial wave functions with parameters. By adjusting parameters according to variational principles one obtains optimal wave function. For the trial wave function for fermionic systems, a Slater determinant is often used with Gutzwiller-Jastrow type correlation factor to reflect correlation effects. Monte Carlo sapling is used in computing expectation values. Hence the name of the method. Because of the absence of the negative sign problem, this method is applicable to a broad range of problems including the first principles calculation (e.g., CASINO), quantum chemistry (e.g., QWalk), lattice fermion systems (e.g., mVMC), etc.