A continuous-state branching processes in random environment(CBRE-process)is defined as the strong solution of a stochastic integral equation.The environment is determined by a Levy process with no jump less than-1.We give characterizations of the quenched and annealed transition semigroups of the process in terms of a backward stochastic integral equation driven by another Levy process determined by the environment.The process hits zero with strictly positive probability if and only if its branching mechanism satisfies Greys condition.In that case,a characterization of the extinction probability is given using a random differential equation with singular terminal condition.The strong Feller property of the CBRE-process is established by a coupling method.We also prove a necessary and sufficient condition for the ergodicity of the subcricital CBRE-process with immigration.This is a joint work with Hui He and Wei Xu.