We present an overview of observational and theoretical evidence of chaos and intermittency in the solar-terrestrial environment including solar dynamo, solar atmosphere, solar wind, and terrestrial magnetosphere-ionosphere-atmosphere. The chaotic nature of space plasmas is studied by a nonlinear model of Alfv¿n waves described by the low-dimensional limit of the derivative nonlinear Schr¿dinger equation given by its stationary solutions in the frame moving with the driver wave velocity. A periodic window of the bifurcation diagram is constructed to identify two types of Alfv¿n chaos related to type-I intermittency and crisis-induced intermittency. We show that an Alfv¿n chaotic attractor is composed of chaotic saddles and unstable periodic orbits and explain the links between these unstable structures and Alfv¿n intermittency. The role of interplanetary Alfv¿n intermittency in the solar wind driving of intense geomagnetic activities is discussed.