We introduce the fundamental aspects of topological spin textures in magnetism, topological spin crystals, the emergent electromagnetic fields arising from the Berry phase, and the resultant transport and optical phenomena. Starting from the homotopy group for classical spins in one, two, and three dimensions, we introduce various topological spin textures corresponding to each dimension. Then, we introduce an important observation that these topological spin textures can form a periodic lattice structure, called topological spin crystals, and such crystal structures are represented by the superposition of multiple spin density waves. Then, we introduce the emergent electromagnetic fields arising from the Berry phase and the resultant electronic transport and optical properties, serving as a probe of topological spin textures. We also briefly review the experimental studies on the topological spin crystals, focusing on one-dimensional chiral soliton lattices, two-dimensional skyrmion lattices, and three-dimensional hedgehog lattices. In addition, we discuss three stabilization mechanisms for such topological spin crystals. Finally, we present the motivation of our study.