We study the stochastic formulation of chemical and biochemical kinetics as an alternative to the ordinary differential equations (ODE).  In the large-system limit, the chemical master equation (CME) tends to the traditional ODE based on the law of mass actions.  Nonlinear chemical oscillations correspond to rotational random walks.  We introduce the concept of nonequilibrium steady-state (NESS) and develop a statistical thermodynamic theory characterized by the positive entropy production. Application of this approach to cellular biochemical systems and signal transduction processes are discussed.