Under the envisioned smart city paradigm, there is an increasing demand for the coordinated operation of our infrastructure networks. In this context, this thesis puts forth a comprehensive toolbox for the optimization of electric power and water distribution networks. On the analytical front, the toolbox consists of novel mixed-integer (non)-linear program (MINLP) formulations; convex relaxations with optimality guarantees; and the powerful technique of McCormick linearization. On the application side, the developed tools support the operation of each of the infrastructure networks independently, but also towards their joint operation. Starting with water distribution networks, the main difficulty in solving any (optimal-) water flow problem stems from a piecewise quadratic pressure drop law. To efficiently handle these constraints, we have first formulated a novel MINLP, and then proposed a relaxation of the pressure drop constraints to yield a mixed-integer second-order cone program. Further, a novel penalty term is appended to the cost that guarantees optimality and exactness under pre-defined network conditions. This contribution can be used to solve the WF problem; the OWF task of minimizing the pumping cost satisfying operational constraints; and the task of scheduling the operation of tanks to maximize the water service time in an area experiencing electric power outage. Regarding electric power systems, a novel MILP formulation for distribution restoration using binary indicator vectors on graph properties alongside exact McCormick linearization is proposed. This can be used to minimize the restoration time of an electric system under critical operational constraints, and to enable a coordinated response with the water utilities during outages. / Master of Science / The advent of smart cities has promoted research towards interdependent operation of utilities such as water and power systems. While power system analysis is significantly developed due to decades of focused research, water networks have been relying on relatively less sophisticated tools. In this context, this thesis develops Advanced efficient computational tools for the analysis and optimization for water distribution networks. Given the consumer demands, an optimal water flow (OWF) problem for minimizing the pump operation cost is formulated. Developing a rigorous analytical framework, the proposed formulation provides significant computational improvements without compromising on the accuracy. Explicit network conditions are provided that guarantee the optimality and feasibility of the obtained OWF solution. The developed formulation is next used to solve two practical problems: the water flow problem, that solves the complex physical equations yielding nodal pressures and pipeline flows given the demands/injections; and an OWF problem that finds the best operational strategy for water utilities during power outages. The latter helps the water utility to maximize their service time during power outages, and helps power utilities better plan their restoration strategy. While the increased instrumentation and automation has enabled power utilities to better manage restoration during outages, finding an optimal strategy remains a difficult problem. The operational and coordination requirements for the upcoming distributed resources and microgrids further complicate the problem. This thesis develops a computationally fast and reasonably accurate power distribution restoration scheme enabling optimal coordination of different generators with optimal islanding. Numerical tests are conducted on benchmark water and power networks to corroborate the claims of the developed formulations.