  In modern science, computer models are often used to understand complex
phenomena, and a thriving statistical community has grown around analyzing
them. This review aims to bring a spotlight to the growing prevalence of
stochastic computer models -- providing a catalogue of statistical methods for
practitioners, an introductory view for statisticians (whether familiar with
deterministic computer models or not), and an emphasis on open questions of
relevance to practitioners and statisticians. Gaussian process surrogate models
take center stage in this review, and these, along with several extensions
needed for stochastic settings, are explained. The basic issues of designing a
stochastic computer experiment and calibrating a stochastic computer model are
prominent in the discussion. Instructive examples, with data and code, are used
to describe the implementation of, and results from, various methods.
