Chemical reactions and diffusion are two basic mechanisms governing the dynamics of molecules in a fluid. As such, they play a critical role in molecular communication for channel modeling, design of detection rules, implementation of molecular circuits for computation, and modeling interactions with external biochemical systems. For finite numbers of information-carrying molecules, stochastic models naturally arise with the simplest example given by the Wiener process, often known as Brownian motion. Nevertheless, the Wiener process fails to be accurate when external forces, friction, and chemical reactions are present. Recently, there have been several contributions that tailor molecular communication systems to these more challenging channel conditions. In this paper, we first overview a general family of stochastic models of reaction and diffusion systems, including both Langevin diffusion and the reaction-diffusion master equation. These models form a basis for the use of these models as molecular communication channels, from which modulation and detection schemes can be developed. We survey recent results on the design of these schemes, with a focus on a recently developed approach which is robust to a wide range of channel models, known as equilibrium signaling. We then turn to the implementation of these detection schemes and related parameter estimation problems via stochastic molecular circuits, based on stochastic chemical reaction networks. Finally, interactions between molecular communication systems and stochastic biological systems as well as open problems are discussed. Our overarching goal is to highlight how the consideration of general stochastic models of reaction and diffusion can be utilized in order to widen the application of molecular communications both within engineered systems, and also as motivation for advances in the mathematical characterization of these models.

化学反应和扩散是控制流体中分子动力学的两种基本机制。因此，它们在通道建模的分子通信、检测规则的设计、用于计算的分子电路的实现以及与外部生化系统的相互作用建模方面发挥着关键作用。对于有限数量的携带信息的分子，随机模型自然会出现在维纳过程给出的最简单的例子中，通常称为布朗运动。然而，当存在外力、摩擦和化学反应时，维纳过程不能准确。最近，有一些贡献可以针对这些更具挑战性的通道条件定制分子通信系统。在本文中，我们首先概述了一系列反应和扩散系统的随机模型，包括朗之万扩散和反应扩散主方程。这些模型构成了将这些模型用作分子通信通道的基础，从中可以开发调制和检测方案。我们调查了这些方案设计的最新结果，重点是最近开发的一种方法，该方法对广泛的信道模型具有鲁棒性，称为均衡信号。然后，我们转向基于随机化学反应网络，通过随机分子电路实现这些检测方案和相关参数估计问题。最后，讨论了分子通信系统和随机生物系统之间的相互作用以及开放问题。