The spin Seebeck effect (SSE) refers to the generation of a spin current as a result of a temperature gradient in a magnetic material, which can be detected electrically via the inverse spin Hall effect in a metallic contact. Since the discovery of SSE in 2008, intensive studies on SSE have been conducted to elucidate its origin. SSEs appear in a wide range of magnetic materials including ferro-, ferri-, and antiferro-magnets and also paramagnets with classical or quantum spin fluctuation. SSE voltage reflects fundamental properties of a magnet, such as elementary excitation, static magnetic order, spin correlation, and spin transport. In this article, we review recent progress on SSEs in various systems, with particular emphasis on its emerging role as a probe of these magnetic properties in solids. We also briefly discuss the recently-discovered nuclear SSE.