Urban drainage systems are in general failing in their functions mainly due to non-stationary climate and rapid urbanization. As these systems are becoming less efficient, issues such as sewer overflows and increase in urban flooding leading to surge in pollutant loads to receiving water bodies are becoming pervasive rapidly. A comprehensive investigation is required to understand these factors impacting the functioning of urban drainage, which vary spatially and temporally and are more complex when weaving together. It is necessary to establish a cost-effective, integrated planning and design framework for every local area by incorporating fit for purpose alternatives. Carefully selected adaptive measures are required for the provision of sustainable drainage systems to meet combined challenges of climate change and urbanization. This paper reviews challenges associated with urban drainage systems and explores limitations and potentials of different adaptation alternatives. It is hoped that the paper would provide drainage engineers, water planners, and decision makers with the state of the art information and technologies regarding adaptation options to increase drainage systems efficiency under changing climate and urbanization.