Despite the plethora of studies reported during the last decade in relation to educational innovation in teaching and assessment of competencies, a consensus is seemingly lacking on a definition that establishes the scope and boundaries competency assessment. This research gap motivated a systematic review of the literature published on the topics of “educational innovation in teaching” and “assessment of competencies” in upper secondary and higher education during the period from January 2016 to March 2021. The main objective of the study was to define and evaluate educational innovation in teaching and assessment of competencies in upper secondary and higher education following PRISMA guidelines for a systematic literature review (SLR) on a curated corpus of 320 articles. We intended to answer the following questions: (1) What do “educational innovation in teaching” and “assessment of competencies” represent for upper secondary and higher education? (2) How are they evaluated? Lastly, (3) are efforts exerted toward the standardization of transversal competencies? The SLR seeks answers to these questions by examining nine research sub-queries. The result indicated that the greatest effort toward educational innovation in competencies was made at the higher education level and targeted students. Competencies were revised through associations with the Sustainable Development Goals of the 2030 Agenda. In addition, the methodologies used for teaching and evaluation of competencies were reviewed. Finally, the study discussed which technologies were used to develop the proficiencies of students.