This paper delves into the expansive world of cellular automata (CA), abstract models of computation comprised of cells that interact based on predefined rules. Originating from John von Neumann’s work in the 1940s, CA has evolved into a multidisciplinary field with applications ranging from mathematical concepts to complex simulations of biological, physical, computer science, material science, and social systems. The paper reviews its historical development, emphasizing John Conway’s influential Game of Life and Burk’s seminar collection. The authors categorize and explore a myriad of CA topics, including self-replicating automata, the universality of computation, compromises in CA, variants, applications in biological systems, fault-tolerant computation, pattern recognition, CA games, fractals, dynamic properties, complexity, image processing, cryptography, bioinformatics, materials modeling, probabilistic automata, and contemporary research. The significance of cellular automata for materials modeling cannot be overstated and considerable attention has been devoted to the issues of modeling nucleation and recrystallization. The review aims to provide a comprehensive resource for both beginners and experts in the field, shedding light on cellular automata’s dynamic and diverse applications in various aspects of life and scientific inquiry.