The EU project 'Assess Inquiry in Science, Technology and Mathematics Education' (ASSIST-ME) investigates formative and summative assessment methods to support and improve inquiry-based approaches in European science, technology and mathematics (STM) education. In the first step of the project, a literature review was conducted in order to gather information about the current state of the art in formative and summative assessment in inquiry-based education (IBE) in STM. This report is the output of Pearson’s work on this with the purpose of provide a literature review that will inform the development of digital assessments which are relevant to the aims of ASSIST-ME. The objectives of the report is to through the literature identify relevant theories and models, identify strategies used in the evaluation of the models which could inform good practice, identify existing relevant digital assessments, and to identify implications for the development of the digital assessments relevant to the aims of ASSIST-ME.