Continuous-state branching processes are continuous-state counterparts of discrete-state Bienayme-Galton-Watson branching processes. We consider a class of continuous-state branching processes with branching rates depending on the current population sizes. They are nonnegative-valued Markov processes that can be obtained either from spectrally positive Levy processes via Lamperti type time changes or as unique nonnegative solutions to SDEs driven by Brownian motion and (or) Poisson random measure with positive jumps. The nonlinear branching mechanism allows the processes to have exotic behaviours such as coming down from innity. But at the same time it brings in new challenges to their study for lack of the additive branching property. In this talk we introduce the above continuous-state nonlinear branching processes, and present results on coming down from innity, explosion and extinguishing behaviours for such processes. It is based on joint work with Clement Foucart, Bo Li, Junping Li, Pei-Sen Li and Yingchun Tang.