Structure features play an important role in machine learning models for the materials investigation. Here, two topology-based features for the representation of material structure, specifically structure graph and algebraic topology, are introduced. We present the fundamental mathematical concepts underlying these techniques and how they encode material properties. Furthermore, we discuss the practical applications and enhancements of these features made in specific material predicting tasks. This review may provide suggestions on the selection of suitable structural features and inspire creativity in developing robust descriptors for diverse applications.