Elastic fibres are critical constituents of dynamic biological structures that functionally require elasticity and resilience. The network of elastic fibres in the anulus fibrosus of the intervertebral disc is extensive, however until recently, the majority of histological, biochemical and biomechanical studies have focussed on the roles of other extracellular matrix constituents such as collagens and proteoglycans. The resulting lack of detailed descriptions of elastic fibre network architecture and mechanical function has limited understanding of the potentially important contribution made by elastic fibres to healthy disc function and their possible roles in the progression of disc degeneration. In addition, it has made it difficult to postulate what the consequences of elastic fibre related disorders would be for intervertebral disc behaviour, and to develop treatments accordingly. In this paper, we review recent and historical studies which have examined both the structure and the function of the human lumbar anulus fibrosus elastic fibre network, provide a synergistic discussion in an attempt to clarify its potentially critical contribution both to normal intervertebral disc behaviour and the processes relating to its degeneration, and recommend critical areas for future research.