Partial differential equations (PDEs) are one of the most important modeling paradigms in science and engineering. For enabling a sophisticated use of these PDE models, the optimal control, design, calibration, and inversion of them is indispensable. The resulting optimization problems with PDE constraints form a challenging class of optimization problems. Tackling them suitably requires a close interplay of theory and numerics for both PDEs and optimization. Often, further challenges, such as nonsmoothness or random inputs enter the scene. Also, machine learning components are increasingly being incorporated into PDE models. This minisymposium addresses, from different angles, new solution approaches to the many challenges in PDE-constrained optimization.