Likelihood-based inference tends to be computationally intensive or wholly intractable for many common models in spatial statistics. Examples include Gaussian processes for large data sets and models for spatial extremes. Recent work has used neural networks to predict parameters in these models, circumventing the intractability of likelihood computations. Prediction, however, depends on the choice of a prior on the parameters and does not provide a straightforward means for frequentist uncertainty quantification. In this talk, I will demonstrate how to use tools from likelihood-free inference to learn the likelihood function of intractable spatial processes using convolutional neural networks. In cases where the exact likelihood is available, the method provides similar point estimation and uncertainty quantification performance as exact likelihood computations at a fraction of the computational cost. When the likelihood is unavailable, this method can learn the otherwise intractable likelihood function, providing inferences that are superior to existing approximations. The method is applicable to any spatial process on a grid from which fast forward simulations are available.