Electromagnetic (EM) solvers are of paramount importance to simulate the behavior of complex microwave and photonic devices and systems, which have many applications in domains as communication, sensing, imaging, and computing. However, EM solvers can result very computationally expensive. In a design flow it is needed to carry out design tasks such as optimization and uncertainty quantification, and therefore a high number of EM simulations can be required. The direct use of EM solvers into a design flow then can easily become unfeasible. Advanced data-driven modeling techniques have been proposed for simulation and design of microwave and photonic devices and systems. These modeling techniques can be used to tremendously speed-up the design flow while retaining high accuracy in the obtained results. Multiple applications will be presented where different modeling techniques are used for a variety of devices and systems of interest (e.g., microwave filters, antennas, metasurfaces for (bio)imaging and communication, electronic circuits, etc.) and can be tailored towards optimization and uncertainty quantification.