Computer models are used as surrogates for physical experiments in a large variety of applications. Nevertheless, the number of evaluations of the computer model is often severely limited due to the complexity and cost of the model. As a result, Gaussian process regression has proven to be a useful statistical emulator for complex computer experiments. However, even this statistical emulator can be very expensive for large designs, since the matrix calculations involved in evaluating the likelihood become intractable. We present an overview of the methods that have been proposed for overcoming this issue, and compare their performance in a variety of settings.