Structural anisotropy is a hallmark of many tissues in humans. The spatially aligned organization of cells and extracellular matrix (ECM) is crucial to physiological functions such as contraction (muscle, myocardium), locomotion (tendon, muscle) and sight (cornea). Restoration of tissue anisotropy lost due to injury or disease is thus a fundamental - yet overlooked - aspect of functional tissue regeneration. In vivo, tissue anisotropy develops from cell patterning and subsequent ECM synthesis and organization and is influenced by ECM remodelling. By contrast, regenerative bioengineering strategies often dictate tissue anisotropy by providing cues that direct cells and ECM during neo-tissue formation, for example, by implanting resorbable scaffolds that present such cues. However, in vivo regeneration, development and remodelling of the new tissue might influence the intended tissue layout, rendering the engineered tissues dysfunctional. Thus, strategies for restoring tissue anisotropy could benefit from improved understanding of tissue structural evolution and the manipulation thereof using external cues. Here, we summarize the development of structural anisotropy in native tissues, followed by in vitro reductionist approaches to understand and gear the driving forces of cell and tissue anisotropy. Translating these insights to in vivo contexts, we discuss knowledge gaps and propose new research directions for the bioengineering of structural anisotropy in damaged tissues.