An infinite element is the one that can handle a domain of infinity. Itis a special finite element, and can have aseamless connection with convertional finite elements. It can be a mapped infiniteelement or a non-mapped infinite element. The former, such as Bettess element and Astley element, needsgeometry mapping and shape functions in terms of local coordinates,while for the latter, the shape functions are directly expressed in terms of global coordinates. This paper reviews thestate-of-the-art and recent advances of the infinite element methodfor unbounded domains. First, the concept and features of the infinite element method are introduced. Then, taking thewave problems governed by the Helmholtz equation as an example, severalconventional infinite elements such as the Bettess element, the Astleyelement and the Burnett element are compared and reviewed. Next, weintroduce the generalized infinite element and its relation to the conventional infinite elements. Finally, the applications of theinfinite element to various problems are summarized.