Brain networks are increasingly understood as information processing systems with modular and hierarchically modular structures. Modular networks consist of densely connected submodules with sparse interconnections. Brain networks often have anatomically or functionally related regions as modules, with inter-module connections being long-distance. Hierarchical modularity refers to modular structures at multiple scales, with modules containing submodules. Modular and hierarchically modular networks offer advantages like robustness, adaptability, and evolvability. This review discusses mathematical concepts for analyzing modularity in brain networks and recent studies on structural and functional brain networks derived from neuroimaging data. Modularity is a key property of many complex systems, including the brain. It is characterized by dense intra-module connections and sparse inter-module connections. Modular networks have higher clustering and shorter path lengths, making them small-world networks. Hierarchical modularity is a fractal property, with similar community structures at different levels. Brain networks exhibit hierarchical modularity, with modules within modules, and self-similarity across scales. Modular organization in brain networks is supported by theoretical and empirical evidence. Modular networks are efficient in information processing, with high clustering and short path lengths. They allow for localized processing of specialized functions and global integration of more general functions. Modular networks also support dynamical complexity and transient states. The development of brain networks is associated with the formation of modules, with modules specializing in sub-problems and allowing for rapid adaptation. Modularity in brain networks is supported by anatomical and functional evidence. Anatomically, specialized functions are localized in specific brain regions. Functionally, brain networks are decomposed into functionally connected regions. Modular organization is also supported by psychological theories, such as phrenology, which suggest that mental functions can be divided into modules. Modularity can be measured using various methods, including modularity metrics and community detection algorithms. These methods help identify modules and quantify their modularity. Modularity is often compared to null models to assess significance. Modularity analysis has been applied to both anatomical and functional brain networks, revealing consistent modular structures. Modular organization in brain networks is also supported by hierarchical modularity, with modules within modules. Hierarchical modularity is a fractal property, with similar community structures at different levels. Brain networks exhibit hierarchical modularity, with modules within modules, and self-similarity across scales. Future research should explore the relationship between topological modularity and other aspects of modularity, such as physical, developmental, pathological, or psychological aspects. Understanding how modularity relates to brain function and disease is an important area of research. Modularity may be disrupted in neuropsychiatric disorders, supporting abnormal modularity as a diagnostic biomarker. The relationship between topological modularity and psychological modularity is also an important area of study.Brain networks are increasingly understood as information processing systems with modular and hierarchically modular structures. Modular networks consist of densely connected submodules with sparse interconnections. Brain networks often have anatomically or functionally related regions as modules, with inter-module connections being long-distance. Hierarchical modularity refers to modular structures at multiple scales, with modules containing submodules. Modular and hierarchically modular networks offer advantages like robustness, adaptability, and evolvability. This review discusses mathematical concepts for analyzing modularity in brain networks and recent studies on structural and functional brain networks derived from neuroimaging data. Modularity is a key property of many complex systems, including the brain. It is characterized by dense intra-module connections and sparse inter-module connections. Modular networks have higher clustering and shorter path lengths, making them small-world networks. Hierarchical modularity is a fractal property, with similar community structures at different levels. Brain networks exhibit hierarchical modularity, with modules within modules, and self-similarity across scales. Modular organization in brain networks is supported by theoretical and empirical evidence. Modular networks are efficient in information processing, with high clustering and short path lengths. They allow for localized processing of specialized functions and global integration of more general functions. Modular networks also support dynamical complexity and transient states. The development of brain networks is associated with the formation of modules, with modules specializing in sub-problems and allowing for rapid adaptation. Modularity in brain networks is supported by anatomical and functional evidence. Anatomically, specialized functions are localized in specific brain regions. Functionally, brain networks are decomposed into functionally connected regions. Modular organization is also supported by psychological theories, such as phrenology, which suggest that mental functions can be divided into modules. Modularity can be measured using various methods, including modularity metrics and community detection algorithms. These methods help identify modules and quantify their modularity. Modularity is often compared to null models to assess significance. Modularity analysis has been applied to both anatomical and functional brain networks, revealing consistent modular structures. Modular organization in brain networks is also supported by hierarchical modularity, with modules within modules. Hierarchical modularity is a fractal property, with similar community structures at different levels. Brain networks exhibit hierarchical modularity, with modules within modules, and self-similarity across scales. Future research should explore the relationship between topological modularity and other aspects of modularity, such as physical, developmental, pathological, or psychological aspects. Understanding how modularity relates to brain function and disease is an important area of research. Modularity may be disrupted in neuropsychiatric disorders, supporting abnormal modularity as a diagnostic biomarker. The relationship between topological modularity and psychological modularity is also an important area of study.