Artificial Intelligence is at the heart of modern society with computers now capable of making process decisions in many spheres of human activity. In education, there has been intensive growth in systems that make formal and informal learning an anytime, anywhere activity for billions of people through online open educational resources and massive online open courses. Moreover, new developments in Artificial Intelligence-related educational assessment are attracting increasing interest as means of improving assessment efficacy and validity, with much attention focusing on the analysis of the large volumes of process data being captured from digital assessment contexts. In evaluating the state of play of Artificial Intelligence in formative and summative educational assessment, this paper offers a critical perspective on the two core applications: automated essay scoring systems and computerized adaptive tests, along with the Big Data analysis approaches to machine learning that underpin them.