In this talk, I will present an accessible introduction to topological data analysis (TDA), with a focus on its integration with statistical methodologies. TDA techniques can be broadly grouped into two categories: feature extraction and data visualization. Feature extraction methods aim to identify topological characteristics of data that, with suitable preprocessing, can be incorporated into standard statistical workflows. Key tools in this category include persistent homology, Euler characteristic curves and profiles. I will introduce these concepts and demonstrate how they complement classical statistical techniques. In particular, I will discuss TopoTests, a method that utilizes topological features to address the problem of goodness-of-fit testing. The second category of TDA methods focuses on visualization, helping analysts uncover the structure of their data and select appropriate methods for further analysis. This includes tools such as Mapper, Ball Mapper, and the recently developed ClusterGraph. I will present these techniques and compare them to traditional approaches in dimensionality reduction and data visualization.