Spatial networks are networks where nodes and edges are embedded in space, and space significantly influences their structure and properties. Examples include transportation, internet, power grids, and social networks. Space introduces costs associated with edge lengths, affecting the topology of these networks. This review explores the current understanding of spatial networks, empirical observations, and models. It discusses processes like phase transitions, random walks, synchronization, navigation, resilience, and disease spread on spatial networks. Spatial networks are often planar, with nodes and edges embedded in two or three dimensions. Planar networks have specific properties, such as Euler's formula (N - E + F = 2), and their structure is influenced by spatial constraints. Voronoi tessellations provide a natural null model for spatial networks. Spatial networks mix topology and space, requiring specific tools for characterization. Empirical observations show that spatial networks have distinct properties, such as transportation networks, infrastructure networks, mobility networks, and neural networks. These networks exhibit stylized facts, such as heterogeneity in degree distributions and clustering coefficients. Spatial networks often have a flat assortativity function, indicating a lack of strong degree correlations. Models of spatial networks include random geometric graphs, spatial generalizations of Erdos-Renyi graphs, spatial small-world models, and optimal networks. These models help understand how spatial constraints affect network properties. Processes on spatial networks, such as Ising models, random walks, synchronization, navigation, and disease spread, are influenced by spatial structure. The review highlights the importance of spatial networks in various fields, including urbanism, epidemiology, and neuroscience. It discusses the effects of space on network properties, such as the efficiency of routing, resilience, and disease spread. The review also addresses open problems in the study of spatial networks, emphasizing the need for further research.Spatial networks are networks where nodes and edges are embedded in space, and space significantly influences their structure and properties. Examples include transportation, internet, power grids, and social networks. Space introduces costs associated with edge lengths, affecting the topology of these networks. This review explores the current understanding of spatial networks, empirical observations, and models. It discusses processes like phase transitions, random walks, synchronization, navigation, resilience, and disease spread on spatial networks. Spatial networks are often planar, with nodes and edges embedded in two or three dimensions. Planar networks have specific properties, such as Euler's formula (N - E + F = 2), and their structure is influenced by spatial constraints. Voronoi tessellations provide a natural null model for spatial networks. Spatial networks mix topology and space, requiring specific tools for characterization. Empirical observations show that spatial networks have distinct properties, such as transportation networks, infrastructure networks, mobility networks, and neural networks. These networks exhibit stylized facts, such as heterogeneity in degree distributions and clustering coefficients. Spatial networks often have a flat assortativity function, indicating a lack of strong degree correlations. Models of spatial networks include random geometric graphs, spatial generalizations of Erdos-Renyi graphs, spatial small-world models, and optimal networks. These models help understand how spatial constraints affect network properties. Processes on spatial networks, such as Ising models, random walks, synchronization, navigation, and disease spread, are influenced by spatial structure. The review highlights the importance of spatial networks in various fields, including urbanism, epidemiology, and neuroscience. It discusses the effects of space on network properties, such as the efficiency of routing, resilience, and disease spread. The review also addresses open problems in the study of spatial networks, emphasizing the need for further research.