Despite early cartographical and graph-theoretical analyses of maritime flows in the 1940s and 1960s, it is only from the 2000s onwards that maritime network analysis had grown apace, backed by newly available shipping data, increased computational power, and renewed conceptual frameworks to study networks in general. The evolution of maritime network analysis, in geography and other sciences, is marked by a wide diversity of methods and themes, which we classify into three main parts. We first present studies looking at maritime flows in an abstract space, focusing on operational, statistical, or managerial aspects where navigation, graph structure, and firms' strategies are the key concerns. Second, we review researches where maritime flows and networks are markers and vectors of wider geo-economic structures and dynamics, such as regional inequalities and areas of dominance. Lastly, maritime networks have also been considered as integral parts of territories and wider chained systems, such as urban networks, regional networks, and coupled networks. We conclude that network analysis and maritime transport still share many uncovered areas and discuss potential research pathways for future works.