The rapid growth of the robotics industry highlights a critical need for skilled graduates, a challenge that falls to higher education. However, the multidisciplinary nature of robotics, which spans areas from mathematics and control theory to machine learning, complicates curriculum development and instructor recruitment. While synthesizing pedagogical literature offers a solution, existing reviews primarily focus on using robotics to teach other subjects rather than on methods for teaching robotics itself. Addressing this gap, this paper presents a review of pedagogical practices and technological innovations in robotics education over the past decade, with a specific focus on higher education. Its contributions are threefold: (a) a dedicated analysis of tertiary-level education, distinguishing it from the K-12 outreach; (b) an analysis of emerging trends in the literature; and (c) a synthesis of innovations and practices mapped to core elements of robotics knowledge. This review aims to provide a foundational resource for enhancing robotics curriculum design and instruction.