Technology-based, open-ended learning environments (OELEs) can capture detailed information of students' interactions as they work through a task or solve a problem embedded in the environment. This information, in the form of log data, has the potential to provide important insights about the practices adopted by students for scientific inquiry and problem solving. How to parse and analyse the log data to reveal evidence of multifaceted constructs like inquiry and problem solving holds the key to making interactive learning environments useful for assessing students' higher-order competencies. In this paper, we present a systematic review of studies that used log data generated in OELEs to describe, model and assess scientific inquiry and problem solving. We identify and analyse 70 conference proceedings and journal papers published between 2012 and 2021. Our results reveal large variations in OELE and task characteristics, approaches used to extract features from log data and interpretation models used to link features to target constructs. While the educational data mining and learning analytics communities have made progress in leveraging log data to model inquiry and problem solving, multiple barriers still exist to hamper the production of representative, reproducible and generalizable results. Based on the trends identified, we lay out a set of recommendations pertaining to key aspects of the workflow that we believe will help the field develop more systematic approaches to designing and using OELEs for studying how students engage in inquiry and problem-solving practices.