The present work reviews the main challenges regarding adaptation of urban drainage networks to climate change by comparing 32 case studies from 29 articles, published between 2003 and 2020. The aim is to: (i) identify the state-of-the-art scientific approaches of adaptation of urban drainage networks to climate change; (ii) assess whether or not these approaches incorporated monetization of the adaptation practices and the associated costs/benefits; and (iii) define a novel approach (Blueprint) for the future development and assessment of urban drainage network adaptation to climate change and other drivers. First, the motivation is provided that makes urban drainage adaptation a globally relevant issue. Second, the main impacts of climate change on precipitation, flooding and urban drainage systems are discussed. Then, current practices are described. Finally, a blueprint for an integrated urban adaptation framework to climate change and other drivers is proposed. Our research indicated that future quantity and quality of urban runoff is not widely addressed in the scientific literature. The Storm Water Management Model is the most widely used software in modeling adaptation options. Solutions such as plans of maintenance and rehabilitation, public awareness, flood forecasting and warning, mobility measures and insurance measures are not widely reflected in the literature. Uncertainties of climate projections and bias correction methods are still significant, and uncertainties of socio-economic scenarios, hydrologic and hydrodynamic models, and adaptation options are not fully addressed. Finally, environmental cost and benefits associated with the ecosystem services provided by the adaptation options are not fully addressed.