Peer assessment is a valuable educational activity, which promotes learner engagement and critical thinking, while also decreasing the time spent by the teachers on evaluating students' work. Over the past decades, several platforms have been proposed to support the peer assessment process. The current landscape is dominated by special-purpose, context-specific peer evaluation systems, which were designed to support a particular type of learning activity, artifact, or discipline. In this article, we propose an alternative, a generic and comprehensive peer assessment platform, called LearnEval, which is very flexible and able to accommodate a variety of pedagogical scenarios. Distinctive functionalities include: highly configurable peer assessment workflow, several automatic and manual review allocation mechanisms, initial calibration/training options for the students, complex dashboard with statistics, scores and graphical visualizations, as well as an extensive open learner model. The platform was developed in an iterative manner, with several extensions and improvements informed by the findings of the initial pilot studies. The article also reports on a practical application of LearnEval in a project-based learning scenario, with very promising results; multiple perspectives of the peer assessment process are analyzed: student behavior, peer grades validity, and perceived learning experience. Comparative results with an earlier study show increased levels of system usability, grading validity, and student satisfaction.