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Extending two-dimensional structures into the three-dimensional (3D) space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring curvature and 3D shape. In the case of 3D curved magnetic thin films and nanowires the physics is driven by the interplay between exchange and magnetostatic interactions, which contain spatial derivatives in their energy functionals. This makes both interactions sensitive to the appearance of bends and twists in the physical space. Theoretical works predict the curvature-induced effective anisotropy and effective Dzyaloshinskii-Moriya interaction resulting in a multitude of novel effects including magnetochiral effects (chirality symmetry breaking) and topologically induced magnetization patterning. Those 3D magnetic architectures are already proven to be application relevant for life sciences, targeted delivery, realization of 3D spin-wave filters, and magneto-encephalography devices to name just a few. To this end, the initially fundamental topic of the magnetism in curved geometries strongly benefited from the input of the application-oriented community, which among others explores the shapeability aspect of the curved magnetic thin films. These activities resulted in the development of the family of shapeable magnetoelectronics which already includes flexible, printable, stretchable and even imperceptible magnetic field sensorics. The balance between the fundamental and applied inputs into the topic of magnetism in curved geometries is rather unique. This stimulates even further the development of new theoretical methods and novel fabrication/characterization techniques. The synergy will definitely enable us surpassing the exploratory research and will pave the way towards novel device concepts, where the geometry of a functional thin film will play a decisive role in determining the device performance.