Abstract:The topological horseshoe theory is one of the most important ways to study chaos rigorously. With striking geometric clarity, the method bridges the gap between chaotic theory and numerical computation, and has been extensively used in the study of chaotic invariant sets, computer assisted proofs, topological entropy estimation, etc. In order to make more researchers understand this powerful method, we presents a brief review of topological horseshoe this paper. We first introduce the history from Smale’s horseshoe to topological horseshoes, showing their essential feature; and then present some useful theorems, the corresponding conditions and numerical methods, as well as a toolbox called HsTool; then give two examples, the Hénon map and the hyperchaotic Saito circuit, to show how to find horseshoes in practical systems.