Rubrics are assessment guides for grading and giving feedback to students while demonstrating acquired knowledge and skills. In the last decades, rubrics have been all part of the most used learning evaluation tools in higher education. Its use is further well-related to competency-based assessment purposes. Nevertheless, criticism around design and application has been also implemented in certain reports. In order to understand rubrics’ evolution, practice, benefits, and trends, a systematic literature review on rubrics’ design and use has been conducted. Two databases were selected: Scopus and ProQuest Education. Two phases were determined: The first allowed to identify articles related to rubrics’ design and application for almost three decades. 584 articles were found. From these, most cited articles served to give a scope of rubric evolution and trends. The second phase permitted to identify design and use of performance-based evaluation rubrics from 2009 and 2019. Five terms and Boolean combinations were used. A total of 259 articles was found. After analyzing abstracts and content, 11 open access articles on performance-oriented rubric design and application were chosen. As a result, some facts and reflections on rubric design complexity are discussed towards responding to educational challenges related to competency-based assessment contemporary demands: integration of human learning domains going beyond cognition, authenticity, and interdisciplinarity as features that characterize learning design situations, follow students’ progression, educator’s preparation on assessment literacy for responding to CBA demands, and the involvement of experts of the work field in determining essential evaluation indicators as the main topics looking forward to the next decade.