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van der Waals magnetic materials open up exciting possibilities to investigate fundamental spin properties in low-dimensional systems and to build compact functional spintronic structures. This review focuses on the recent progress in two-dimensional(2D) magnets that explore beyond the homogenous magnetically-ordered state, including magnons (spin waves), magnetic skyrmions, and complex magnetic domains. Properties of these spin and topology excitations in 2D magnets provide insights into spin-orbit interactions and other forms of coupling between electrons, phonons, and spin-dependent excitations. Such spin-based quasiparticles can also serve as information carriers for next-generation high-speed computing elements. We will first lay out the general theoretical basis of dynamical responses in magnetic systems, followed by detailed descriptions of experimental progress in magnons and spin textures (including magnetic domains and skyrmions). Discussion on the experimental techniques and future perspectives are also included.