Concentric tube robots (CTRs) have drawn significant research attention over the years, particularly due to their applications in minimally invasive surgery (MIS). Indeed, their small size, flexibility, and high dexterity enable several potential benefits for MIS. Research has led to an increasing number of discoveries and scientific breakthroughs in CTR design, fabrication, control, and applications. Numerous prototypes have emerged from different research groups, each with their own design and specifications. This survey paper provides an overview of the state-of-the-art of the mechatronics aspects of CTRs, including approaches for the design and fabrication of the tubes, actuation unit, and end effector. In addition to the various hardware and associated fabrication methods, we propose to the research community, a unifying way of classifying CTRs based on their actuation unit architecture, as well as a set of specification details for evaluation of future CTR prototypes. Finally, we also aim to highlight the current advancements, challenges, and perspectives of CTR design and fabrication.