Data sets can be considered as geometric objects. For example, a point cloud can be endowed with a metric structure through Euclidean or Lp distances, digital images can be considered as cubical complexes. Furthermore, metric data can be enriched with the normalized counting measure, and graphs and simplicial complexes can be built out of it through Vietoris-Rips, Cech or similar constructions. Thus, one can apply methods coming from fields like Algebraic Topology, Metric Geometry and Optimal Transport to extract geometric information from data. Two important tools of Geometric and Topological Data Analysis are persistence and Reeb graphs. Persistence provides a computable summary of geometric data by observing it through different scales and keeping track of how topological features evolve. The Reeb graph is a construction producing a graph representation of a filtered space. In this talk, I will explain these tools in detail and will describe my work about them.