The recent progress in generating high spin current densities in magnetic nanostructures has made it possible to excite unprecedented magnon densities from which a range of novel magnetodynamical solitons, such as spin wave bullets, magnetic droplets, and dynamical skyrmions can nucleate. In this chapter, these magnetodynamical solitons, and the devices where they can be created and observed - so-called spin torque and spin Hall nano-oscillators are discussed in detail. The solitons form under conditions of magnon-magnon attraction, which arises when the magnetodynamics exhibits negative non-linearity, and the resulting particle-like objects exhibit a rich dynamics including Brownian motion, drift instabilities, perimeter eigenmode excitations, and merging. While originally only observed indirectly using microwave spectroscopy, these solitons can now also be observed directly using scanning transmission x-ray microscopy.