In this review we consider theoretical and experimental results related to the properties of two-dimensional spin-wave (SW) solitons, so-called SW bullets and SW droplets. Such nonlinear self-localized SW modes possess very interesting physical properties, and could have practical applications in modern and future magnonics and spintronics. The experimental and theoretical results presented in this review have undeniably proven the existence of SW bullets in magnetic films and confined magnetic nanostructures (magnetic nanocontacts), and have elucidated the essential distinctions between the properties of the one-dimensional nonlinear SW solitons, two-dimensional nonlinear SW bullets and linear spin wave packets, as well as the possibility of self-generation, parametrical excitation, and phase-conjugation of the SW bullets, similar to the case of the conventional linear spin waves. Also, in this review we presented experimental results demonstrating the nucleation, dynamics, and annihilation of two-dimensional strongly nonlinear SW "droplets" in spin-torque-driven magnetic nanocontacts. The properties of these exotic nonlinear objects are analyzed using recently developed theoretical models and illustrated by micromagnetic numerical simulations.
