This chapter deals with some generalities on discrete models and the singularities and the bifurcations common to invertible and noninvertible maps. It presents two notions specific to noninvertible maps, having a practical interest: that of absorbing domain and of a chaotic domain. The chapter explores map models having vanishing denominators. Dynamics is a concise term referring to the study of time-evolving processes. The corresponding system of equations describing this evolution is called a dynamic system. Nonlinear dynamics is the scientific field concerning the behavior of real systems, linearity being always an approximation. The "strategy" of qualitative methods can be defined noting that the solutions of equations of nonlinear dynamic systems are in general nonclassical, nontabulated, and transcendental functions of mathematical analysis, which are very complex. The study of the problem of structural stability can be considered complete for the two-dimensional autonomous ordinary differential equations.