Data-driven paradigms are well-known and salient demands of future wireless communication. Empowered by big data and machine learning, next-generation data-driven communication systems will be intelligent with the characteristics of expressiveness, scalability, interpretability, and especially uncertainty modeling, which can confidently involve diversified latent demands and personalized services in the foreseeable future. In this paper, we review a promising family of nonparametric Bayesian machine learning methods, i.e., Gaussian processes (GPs), and their applications in wireless communication. Since GPs achieve the expressive and interpretable learning ability with uncertainty, it is particularly suitable for wireless communication. Moreover, it provides a natural framework for collaborating data and empirical models (DEM). Specifically, we first envision three-level motivations of data-driven wireless communication using GPs. Then, we present the background of the GPs in terms of covariance structure and model inference. The expressiveness of the GP model using various interpretable kernel designs is surveyed, namely, stationary, non-stationary, deep, and multi-task kernels. Furthermore, we review the distributed GPs with promising scalability, which is suitable for applications in wireless networks with a large number of distributed edge devices. Finally, we list representative solutions and promising techniques that adopt GPs in wireless communication systems.
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