Swarm robotics is an approach to collective robotics inspired by the self-organized behaviors of social animals. It aims to design robust, scalable, and flexible collective behaviors for large numbers of robots through simple rules and local interactions. This review analyzes the literature from the perspective of swarm engineering, focusing on ideas and concepts that advance swarm robotics as an engineering field and are relevant to real-world applications. Swarm engineering is an emerging discipline that defines systematic procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining swarm robotics systems. Two taxonomies are proposed: one for design and analysis methods, and another for collective behaviors. The review discusses current limitations of swarm robotics as an engineering discipline and suggests future research directions. Swarm robotics systems are characterized by autonomy, environmental interaction, local sensing and communication, lack of centralized control, and cooperation. The review uses these characteristics to distinguish swarm robotics from other multi-robot approaches. The main inspiration for swarm robotics comes from social animals, which exhibit robust, scalable, and flexible behaviors. Robustness is achieved through redundancy and no leader, scalability through local sensing and communication, and flexibility through redundancy and task allocation. Swarm engineering involves systematic application of scientific and technical knowledge to model and specify requirements, design, realize, verify, validate, operate, and maintain swarm robotics systems. The review discusses two main design methods: behavior-based design and automatic design. Behavior-based design involves developing individual robot behaviors iteratively to achieve collective behavior, often inspired by social animals. Automatic design methods include evolutionary robotics and multi-robot reinforcement learning, which allow automatic generation of behaviors without explicit developer intervention. Analysis is essential in engineering processes, involving modeling and simulation of swarm robotics systems. Microscopic models consider individual robots and their interactions, while macroscopic models describe the system as a whole. Rate equations and differential equations are used to model collective behaviors, while classical control and stability theory is applied to prove properties of the swarm. Real-robot experiments are crucial for validating collective behaviors, although they are often conducted in controlled environments. The review classifies collective behaviors into four categories: spatially-organizing behaviors, navigation behaviors, collective decision-making, and other collective behaviors. These behaviors include aggregation, pattern and chain formation, and task allocation. The review highlights the importance of modeling and simulation in understanding and validating swarm robotics systems, and emphasizes the need for further research in swarm engineering to address current limitations and enhance real-world applications.Swarm robotics is an approach to collective robotics inspired by the self-organized behaviors of social animals. It aims to design robust, scalable, and flexible collective behaviors for large numbers of robots through simple rules and local interactions. This review analyzes the literature from the perspective of swarm engineering, focusing on ideas and concepts that advance swarm robotics as an engineering field and are relevant to real-world applications. Swarm engineering is an emerging discipline that defines systematic procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining swarm robotics systems. Two taxonomies are proposed: one for design and analysis methods, and another for collective behaviors. The review discusses current limitations of swarm robotics as an engineering discipline and suggests future research directions. Swarm robotics systems are characterized by autonomy, environmental interaction, local sensing and communication, lack of centralized control, and cooperation. The review uses these characteristics to distinguish swarm robotics from other multi-robot approaches. The main inspiration for swarm robotics comes from social animals, which exhibit robust, scalable, and flexible behaviors. Robustness is achieved through redundancy and no leader, scalability through local sensing and communication, and flexibility through redundancy and task allocation. Swarm engineering involves systematic application of scientific and technical knowledge to model and specify requirements, design, realize, verify, validate, operate, and maintain swarm robotics systems. The review discusses two main design methods: behavior-based design and automatic design. Behavior-based design involves developing individual robot behaviors iteratively to achieve collective behavior, often inspired by social animals. Automatic design methods include evolutionary robotics and multi-robot reinforcement learning, which allow automatic generation of behaviors without explicit developer intervention. Analysis is essential in engineering processes, involving modeling and simulation of swarm robotics systems. Microscopic models consider individual robots and their interactions, while macroscopic models describe the system as a whole. Rate equations and differential equations are used to model collective behaviors, while classical control and stability theory is applied to prove properties of the swarm. Real-robot experiments are crucial for validating collective behaviors, although they are often conducted in controlled environments. The review classifies collective behaviors into four categories: spatially-organizing behaviors, navigation behaviors, collective decision-making, and other collective behaviors. These behaviors include aggregation, pattern and chain formation, and task allocation. The review highlights the importance of modeling and simulation in understanding and validating swarm robotics systems, and emphasizes the need for further research in swarm engineering to address current limitations and enhance real-world applications.