The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets.