Patterned magnetic nanostructures are advanced materials characterized by their unique magnetic properties at the nanoscale, which are the result of tailored geometric configurations and compositional engineering. As interest in nanotechnology continues to grow exponentially, the exploration of patterned magnetic nanostructures turns into a vibrant and critical area of study for both industry professionals and academic researchers. This chapter gives an overview of investigations of standing spin waves (collective spin precessions) in magnetic elements by the technique of ferromagnetic resonance (FMR). The presentation encompasses earlier studies of arrays of magnetic nanodisks and nanorings by cavity-based FMR as well as more recent studies of individual nanodisks and 3D nanovolcanoes by a broadband FMR method which implies the use of a coplanar waveguide. Overall, the chapter outlines the development of FMR studies along the two major lines: (i) downscaling the system under study from multiple to individual magnetic nanoelements and (ii) extending planar nanomagnets into the third dimension.