In this article we review the recent advances in iterative learning control (ILC) for nonlinear dynamic systems. In the research field of ILC, two categories of system nonlinearities are considered, namely, the global Lipschitz continuous (GLC) functions and local Lipschitz continuous (LLC) functions. ILC for GLC systems is widely studied and analysed using contraction mapping approach, and the focus of recent exploration moves to application problems, though a number of theoretical issues remain open. ILC for LLC systems is currently a hot area and the recent research focuses on ILC design and analysis by means of Lyapunov approach. The objectives of this article are to introduce recent development and advances in nonlinear ILC schemes, highlight their effectiveness and limitations, as well as discuss the directions for further exploration of nonlinear ILC.