The ability of the human lens to accommodate is mediated by the ciliary muscle and zonule; the manifest optical power changes depend on the shape and material properties of the lens. The latter are difficult to measure with accuracy and, given the dynamic aspects of accommodation and the ageing of cells and tissues, the biomechanics of the lens is neither fixed nor constant. A range of techniques have been developed to measure both ageing trends and spatial variations in the mechanical properties and these have yielded a diverse array of findings and respective conclusions. The majority of quasi-static measurements, where the observation time is in minutes or hours, indicate that the stiffness of the lens increases with age at a faster rate in the lens centre than in the periphery. Dynamic measurements show that lens material properties are dependent on the loading frequency. Recent in vivo analyses suggest that, along the optic axis, profiles of elastic moduli are very similar to profiles of refractive index. This review assesses the advantages and limitations of different measurement techniques and consequent variations in elastic moduli that have been found. Consideration is given to the role of computational modelling and the various modelling methods that have been applied. The changes in mechanical properties of the lens associated with ageing and pathology and future implications for implant design are discussed.