The rapid growth of scientific publications necessitates new methods to understand the direction of scientific research within fields of study, ascertain the importance of particular groups, authors, or institutions, compute metrics that can determine the importance (centrality) of particular seminal papers, and provide insight into the social (collaboration) networks that are present. We present one such method based on analysis of citation networks, using the freely available CiteSpace Program. We use citation network analysis on three examples, including a single material that has been widely explored in the last decade (BiFeO3), two small subfields with a minimal number of authors (flexoelectricity and Kitaev physics), and a much wider field with thousands of publications pertaining to a single technique (scanning tunneling microscopy). Interpretation of the analysis and key insights into the fields, such as whether the fields are experiencing resurgence or stagnation, are discussed, and author or collaboration networks that are prominent are determined. Such methods represent a paradigm shift in our way of dealing with the large volume of scientific publications and could change the way literature searches and reviews are conducted, as well as how the impact of specific work is assessed.