Recent years have witnessed a surge in the use of topological objects and methods in various applications. Many such applications leverage either the summarization (e.g, persistent homology) or the characterization power of topological objects. In this talk, we will talk about our graph skeletonization algorithm based on discrete-Morse theory, both for 2D / 3D images or for (high-dimensional) points data. We will then describe that two applications of the resulting algorithms: how the resulting graph skeleton can help us reconstructing or summarizing neurons from 2D / 3D neuronal images, and how to use it to analyze the high dimensional single-cell RNASeq data. This is joint work with many collaborators which we will acknowledge in the talk.