Increasing water demand in the process and its allied industries coupled with global water stress and scarcity has underlined the importance of water as a crucial resource and elevated a need for widespread adoption of water reuse and recycle. This paper provides a state-of-the-art review of the area of water network synthesis focusing on single-site and continuous process problems since its inception in the 1980s. The survey centers around model-based optimization or mathematical programming methods for water network synthesis and covers key findings from the water pinch analysis technique, which are often essential in enhancing model formulations. Major modeling and computational challenges are discussed that explore the issues of nonconvexity, nonlinearity, and uncertainty inherent in water network synthesis problems. The review concludes by providing a perspective of future research directions to be tackled to address the challenges highlighted.