Industries consume large quantities of energy and water in their processes which are often considered to be peripheral to the process operation. Energy is used to heat or cool water for process use; additionally, water is frequently used in production support or utility networks as steam or cooling water. This enunciates the interconnectedness of water and energy and illustrates the necessity of their simultaneous treatment to improve energy and resource efficiency in industrial processes. Since the seminal work of Savulescu and Smith in 1998 introducing a graphical approach, many authors have contributed to this field by proposing graphically- or optimization-based methodologies. The latter encourages development of mathematical superstructures encompassing all possible interconnections. While a large body of research has focused on improving the superstructure development, solution strategies to tackle such optimization problems have also received significant attention. The goal of the current article is to study the proposed methodologies with special focus on mathematical approaches, their key features and solution strategies. Following the convention of Jeżowski, solution strategies are categorized into: decomposition, sequential, simultaneous, meta-heuristics and a more novel strategy of relaxation/transformation. A detailed, feature-based review of all the main contributions has also been provided in two tables. Several gaps have been highlighted as future research directions