Public spaces, and their intimate structural relationship to private spaces, have long been a central interest of urban morphologists. Recent developments in network science have shed new light on the complexity of public space networks, with specific implications for policy, education, and practice. These developments come at a historical moment when all 193 member states of the United Nations have recently adopted by acclamation the New Urban Agenda, a landmark framework agreement for global urbanization through 2036. As it happens, the New Urban Agenda has much to say about public space networks, their structure, and their importance—but implementation remains a historic challenge.