Quantum Monte Carlo methods are the most accurate algorithms for predicting properties of general quantum systems. We briefly introduce ground state, path integral at finite temperature and coupled-electron Monte Carlo methods, their merits and limitations. We then discuss recent calculations using these methods for dense liquid hydrogen as in undergoes a molecular atomic (metal/insulator) transition. We then discuss a procedure that can be used to assess electronic density functionals, which in turn can be used on a larger scale for first principles calculations and apply this technique to dense hydrogen and liquid water.