Abstract: Biological processes occurring at scales of a biological cell can be described in terms of diffusing and interacting molecules. At the level of particle-resolved descriptions, where molecules are represented by particles and chemical reactions are coupled to their spatial diffusion, there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is relatively underdeveloped. In this work, we provide different frameworks to systematically formulate the probabilistic evolution equation, termed chemical diffusion master equation (CDME), that governs stochastic reaction-diffusion processes. Such frameworks can be used to unify reaction-diffusion models at different scales, allowing the development of consistent multiscale simulation schemes. Moreover, these frameworks enable theories, such as stochastic thermodynamics, to be applied to reaction-diffusion processes. This can result in fundamental insights of the physical capabilities and limitations of biological systems and beyond.