The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This paper reviews the observational evidence on climate phenomena and the governing equations of planetary-scale flow, as well as presenting the key concept of a hierarchy of models as used in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and of nonequilibrium statistical physics, on the other, are brought together for the first time and shown to complement each other in helping understand and predict the system's behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.