Artificial Intelligence (AI) based assessments are commonly used in a variety of settings including business, healthcare, policing, manufacturing, and education. In education, AI-based assessments undergird intelligent tutoring systems as well as many tools used to evaluate students and, in turn, guide learning and instruction. This chapter provides a framework for AI-based Assessment (AIBA) in Education that describes systems and tools. The framework comprises five interrelated dimensions that broadly address the purposes and procedures of AIBA for educational technologies: purposes (i.e., summative feedback, formative feedback, training, and instruction), constructs (e.g., knowledge, skills, strategies, and emotion), data sources (e.g., task performance, behaviors, language, and multimodal data), computational methods (e.g., Bayesian statistics, machine learning, and natural language processing), and visibility (e.g., task-related vs. stealth). This chapter describes systems and tools used to provide AIBA and instantiate these tools within these dimensions. Framing systems within these five dimensions of AIBA enables understanding the landscape of tools and systems, and, in turn, pointing to gaps in the literature and future directions. [This chapter was published in: "Handbook of Artificial Intelligence in Education," edited by Benedict du Boulay et al., Edward Elgar Publishing Limited, 2023, pp. 485-504.]