The article provides a comprehensive review of the statistical physics of vaccination, highlighting the historical development and recent advancements in the field. It emphasizes the importance of understanding the interplay between human behavior and disease dynamics, particularly in the context of vaccination. The authors trace the evolution of epidemiological models from classical, homogeneously mixing populations to more complex models that account for heterogeneous contact patterns and behavioral feedback. They discuss the role of statistical physics methods, such as lattice and network models, in understanding the dynamics of infectious diseases. The article also introduces the concept of digital epidemiology, which leverages high-resolution data from sources like social media to model human behavior and disease transmission. Finally, the authors outline open problems and future research directions in the field, emphasizing the need for more sophisticated models that can better predict and control disease outbreaks.The article provides a comprehensive review of the statistical physics of vaccination, highlighting the historical development and recent advancements in the field. It emphasizes the importance of understanding the interplay between human behavior and disease dynamics, particularly in the context of vaccination. The authors trace the evolution of epidemiological models from classical, homogeneously mixing populations to more complex models that account for heterogeneous contact patterns and behavioral feedback. They discuss the role of statistical physics methods, such as lattice and network models, in understanding the dynamics of infectious diseases. The article also introduces the concept of digital epidemiology, which leverages high-resolution data from sources like social media to model human behavior and disease transmission. Finally, the authors outline open problems and future research directions in the field, emphasizing the need for more sophisticated models that can better predict and control disease outbreaks.