For a number of problems in climate dynamics, it is useful to describe the system with a set of macroscopic state variables and consider statistics of the other variables, which may represent highly nonlinear processes, as smooth functions of the macroscopic variables. The utility of a linear approximation to these functions, namely the linear response functions, is illustrated with two examples in atmospheric dynamics. The first is the stability of a moist convecting atmosphere, where the linear response functions are used to elucidate the dynamics of convectively coupled tropical waves and convective self-aggregation. The second example is the dynamics of the annular mode, where the linear response functions are used to quantify the strength of the eddy-mean-flow feedback.