Within the cochlea, broadband sounds are filtered into a series of narrowband signals, each of which has a relatively slowly varying envelope (ENV) imposed on a rapidly oscillating carrier (the temporal fine structure, TFS). Information about ENV and TFS is conveyed in the timing and short-term rate of nerve spikes in the auditory nerve. This paper summarises evidence from studies that allow some separation of the effects of hearing loss and age on the processing of TFS and ENV information. The monaural processing of TFS information seems to be adversely affected by both hearing loss and increasing age. The monaural processing of ENV information is hardly affected by hearing loss or by increasing age. The binaural processing of TFS information is also adversely affected by both hearing loss and increasing age, but here the latter seems more important. The binaural processing of ENV information deteriorates somewhat with increasing age but is not markedly affected by hearing loss. The reduced TFS processing abilities found for older/hearing-impaired subjects may partially account for the difficulties that such subjects experience in complex listening situations.