We discuss how noise as classical stochastic source can be defined precisely from quantum field theory via coarse graining. For open systems where the system and environment are cleary and ab initio separated, one can use the Feynman-Vernon influcence functional to capture the effect of the coarse-grained environment on the system. We show the physical meaning of the noise and dissipation kernels and derive expressions for the noise correlators for different sample field theories, and the functional stochastic equations such as the master, Langevin and Fokker-Planck equations. For a close system such as molecular gas, we start with the Schwinger-Dyson equation but view them in the light of a BBGKY hierarchy. We point out that in realistic physical situations because of the limitation in the measurement accuracy, usually it is the low-order correlation functions which partake in defining the physical system, which we call effectively open systems. We discuss how truncation and factorization without causal initial condition give rise to time-reversal invariant equations of motion of the Vlasov type, where there is no noise and (Landau) `damping' is due to special choices of initial conditions and representation. When causal factorizable (`slaving') conditions such as molecular chaos assumption is imposed, dissipation in the Boltzmann equation appears. We point out that there should also be a noise term accompanying this, arising from the coarse-grained information of the higher order correlations. We derive explicit expressions for such correlation noise via the CTP nPI effective action and arrive at a Boltzmann-Langevin equation. Finally we show under special conditions of near-equilibrium how one can use fluctuation theory in linear response to derive noise in both the open and effectively open systems.