Understanding the organization of molecules in naturally occurring ordered arrays (e.g. membranes, protein fibres and DNA strands) is of great importance to understanding biological function. Unfortunately, few biophysical techniques provide detailed structural information on these non-crystalline systems. UV, visible and IR linear dichroism have the potential to provide such information. Recent advances in technology and simulations allow this potential to be fulfilled, and can now provide a detailed understanding of the molecular mechanisms of such fundamental biological processes as amyloid fibre formation and membrane protein folding.