Small particles exhibit random motions due to collisions by particles composing the surrounding medium. Diffusivity is one of the most important properties for the environment and the target particle. When the environment is heterogeneous and/or the structure of the target particle changes with time, diffusivity becomes a dynamic quantity. These heterogeneous structures are often observed in living cells, entangled polymer, and supercooled liquid, where the diffusivity changes with time. Here, I show analytical results on fluctuations of the observed diffusivity using the paradigmatic stochastic model of a particle diffusion, e.g., the Langevin equation with fluctuating diffusivity. Applying the theoretical results to diffusion of a lipid molecule, a peripheral protein, and supercooled liquids, we show the fluctuating diffusivity provides a novel physical phenomenon. Finally we provide a method to detect transition points at which a state of the target particle or a property of the surrounding environment changes significantly.