Topology interfaces with data science primarily in two ways: by providing robust, deformation-invariant descriptors that quantify theshape and structure of data, and by enabling visualizations of high-dimensional data that preserve topological features. Theseapproaches, grounded in algebraic and combinatorial topology, yield practical tools for data analysis when efficient implemention isprovided.In this talk, I will survey topological methods for analyzing multi-valued data, including constructions based on the Euler characteristic and techniques inspired by phylogenetics. I will also discuss recent developments in applying topological summaries to statistical hypothesis testing, particularly for nonparametric goodness-of-fit testing in high dimensions. Finally, I will explore advanced visualization strategies based on Mapper and its generalizations, which provide interpretable representations of complex data sets. The presentation will focus on both the theoretical foundations and applied outcomes of these techniques.