Due to the openness of the transmission medium, it is necessary for radio systems to have anti-jamming abilities. Traditional anti-jamming methods such as sequence-based frequency hopping and direct sequence spread spectrum have shortcomings of low spectral efficiency and fixed communication patterns. With the development of software-defined radio, jamming devices are increasingly advanced and efficient. In this article, we propose a new paradigm for anti-jamming called DSAJ. With the help of cognitive radio and machine learning, the aim of DSAJ is to learn the dynamic and complex spectrum environment and obtain an optimal communication strategy. We first introduce the basic concept of anti-jamming communications and provide a brief summary of anti-jamming methods. Then, through a case study, mathematical modeling and applications of DSAJ are discussed for both single-user and multi-user systems. A real-life DSAJ testbed is described, and some potential research directions are discussed.