We review modeling and design methods, from mathematical abstractions to data-driven and search-based techniques. Modeling in swarm robotics focuses on reducing dimensionality to abstract and formalize inherently complex systems. A central challenge is local sampling, as robots perceive only limited and unreliable information. Modeling approaches include rate equations, spatial models using ODEs and PDEs (e.g., Langevin, Fokker–Planck), and network-based methods, such as random graphs and adaptive networks. Formal design techniques, including multi-scale modeling and global-to-local programming, address the micro-macro problem of linking local rules to global behavior. Automatic design methods range from data-driven approaches (reinforcement learning, deep learning, imitation learning, and inverse reinforcement learning, as well as large language models) to search-driven optimization (evolutionary algorithms, black-box methods). A persistent challenge across all approaches is the reality gap, the discrepancy between simulated and real-world performance.