In ‘A New Kind of Science’, Stephen WolframWolfram has argued that, to know how a particular cellular automaton (CA) is behaving, one has to observe what is happening just by running the CA. Predicting behavior of a system by means of (mathematical) analysis can only be possible for the special system with simple behavior ([1, p. 6]). In spite of this observation of some researchers, a few characterization tools have been proposed over the years to analyze and predict the behavior of some special classes of cellular automata (CAs). Needless to say, all kinds of dynamic behaviors of a CA may not be analyzed by a tool; but the tools are used to discover some specific properties. In this chapter, three characterization tools—de Bruijn graph, Matrix algebra and Reachability tree are presented for one-dimensional CAs. The de Bruijn graph has been first used to study one-dimensional uniform CA. Later it has been extended to study the non-uniform CA. Whereas, the other two have been primarily developed to study the non-uniform CA. As uniform CAs are the special case of non-uniform CAs, unless otherwise specified, the “CA” refers to the non-uniform CA throughout this chapter.