The main objectives of this chapter are to introduce, exemplify, and discuss the concept of an attractor. We begin by introducing the concept of a fixed point, particularly obtained in a model of a damped oscillator. We then present the concept of a limit cycle. This, in turn, can be obtained from an ordinary differential equation (ODE) containing both a damping term and an external forcing term. We will subsequently discuss the concept of a chaotic attractor using a set of three coupled first-order ODEs. Finally, a last type of attractor is discussed. It has an unusual geometric form, which characterizes it as a strange attractor. However, since the largest Lyapunov exponent—which is one of the indicators of chaos—is negative, the attractor is referred to as a nonchaotic strange attractor.