Gaussian process regression(GPR) is a new machine learning method by the context of Bayesian theory and
statistical learning theory. It provides a flexible framework for probabilistic regression and is widely used to solve the
high-dimensional, small-sample or nonlinear regression problems. Its principle is introduced in the function-space view and
several limitations such as computational difficulties for large data sets and restrictive modelling assumptions for complex
data sets are discussed. Several improved approaches for these limitations are summarized. GPR is simple to implement,
flexible to nonparameter infer and self-adaptive to determinate hyperparameters in comparison with neural network and
support vector machines. The attractive feature that GPR models provide Gaussian uncertainty estimates for their predictions
allows them to be seamlessly incorporated into predictive control, adaptive control and Bayesian filtering techniques. Finally,
its applications are given and future research trends are prospected.