I will give a very brief introduction to large deviation theory, and study the dynamic transition/excursion phenomena in climate systems as a presentation of its application in climate systems. We built a framework using large deviation theory, in which different climate regimes are represented by the statistical most likely states and the transition is described by the most likelihood pathways connecting either metastable states or target sets in the small noise limit. Specifically we considered the energy-constrained stochastic dynamics (equilibrium statistical system), the most likely states of whose invariant measure coincide with the selective decay states. We compute the transition pathways using a constrained String method. Nonequilibrium statistical climate systems were also analyzed where the transition pathways were computed by the geometric minimum action method.