Data-driven paradigms are well-known and salient demands of future wireless communication. Empowered by big data and machine learning techniques, next-generation data-driven communication systems will be intelligent with unique characteristics of expressiveness, scalability, interpretability, and uncertainty awareness, 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 models, i.e., Gaussian processes (GPs), and their applications in wireless communication. Since GP models demonstrate outstanding expressive and interpretable learning ability with uncertainty, they are particularly suitable for wireless communication. Moreover, they provide a natural framework for collaborating data and empirical models (DEM). Specifically, we first envision three-level motivations of data-driven wireless communication using GP models. 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 kernels, including stationary, non-stationary, deep and multi-task kernels, is showcased. Furthermore, we review the distributed GP models 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 GP models in various wireless communication applications.