The connective tissues of the musculoskeletal system can be grouped into fibrous, cartilaginous, and calcified tissues. While each tissue type has a distinct composition and function, the intersections between these tissues result in the formation of complex, composite, and graded junctions. The complexity of these interfaces is a critical aspect of their healthy function, but poses a significant challenge for their repair. In this review, we describe the organization and structure of complex musculoskeletal interfaces, identify emerging technologies for engineering such structures, and outline the requirements for assessing the complex nature of these tissues in the context of recapitulating their function through tissue engineering.