This chapter studies the local convergence and the dynamics of the two-step Newton-like method. It discusses the dynamics of the Newton-like method. The dynamical properties related to an iterative method applied to polynomials give important information about its stability and reliability. The chapter presents the study of the parameter spaces associated to a family of iterative methods, to distinguish between the good and bad methods in terms of its numerical properties. It discusses the basins of attraction of the Newton-like method and also provides numerical examples.