Data exhibiting complicated spatial structures are common in many areas of science (e.g., cosmology, biology), but can be difficult to analyze. Persistent homology is an approach within the area of Topological Data Analysis (TDA) that offers a framework to represent, visualize, and interpret complex data by extracting topological features which may be used to infer properties of the underlying structures. For example, TDA is a beneficial technique for analyzing intricate and spatially complex web-like data such as the large-scale structure (LSS) of the Universe. The output from persistent homology, called persistence diagrams, summarizes the different order holes in the data (e.g., connected components, loops, voids). I will present how persistent homology can be used for inference on LSS and how to locate representations of cosmological voids and filament loops in the original data volume.