There have been significant advances in the last two decades in the development of scaffolds for tissue engineering and regeneration. We now have more bio-interactive materials available and techniques to mimic aspects of the extra cellular matrix (ECM) found in native tissues. A raft of fibre spinning techniques and combinatorial additive manufacture technologies have been developed, and it is now possible to produce complex shapes that exhibit some of the structural hierarchies, mechanical properties and cell guidance cues found in the ECM, as well as incorporate electrically conductive elements for stimulation and sensing. Examples of the spinning technologies in combination with new biomaterials approaches are discussed using skin, the heart, vascular grafts, and peripheral nerve conduits to highlight some of these approaches. The ability to develop biomimetic tissue analogues and micro-tissue models using these tools will enable deeper understanding of cell–material interactions for improved scaffolds, as well as disease modelling and drug screening.