Multienergy systems (MES) can optimally deploy their internal operational flexibility to use combinations of different energy vectors to meet the needs of end-users and potentially support the wider system. Key relevant applications of MES are multienergy districts (MEDs) with, for example, integrated electricity and gas distribution and district heating networks. Simulation and optimization of MEDs is a grand challenge requiring sophisticated techno-economic tools that are capable of modeling buildings and distributed energy resources (DERs) across multienergy networks. This article provides a tutorial-like overview of the state-of-the-art concepts for techno-economic modeling and optimization of integrated electricity-heat-gas systems in flexible MEDs, also considering operational uncertainty and multiple grid support services. Relevant mixed integer linear programming (MILP) formulations for two-stage stochastic scheduling of buildings and DER, iteratively soft-coupled to nonlinear network models, are then presented as the basis of a practical network-constrained MED energy management tool developed in several projects. The concepts presented are demonstrated through real-world applications based on The University of Manchester MED case study, the details of which are also provided as a testbed for future research.