Age-related hearing loss (ARHL), also called presbycusis, is a progressive disorder affecting hearing functions and among the elderly has been recognized as the third most frequent condition. Among ARHL components, the age-related central auditory processing disorder (CAPD) refers to changes in the auditory network, negatively impacting auditory perception and/or the speech communication performance. The relationship between auditory-perception and speech communication difficulties in age-related CAPD is difficult to establish, mainly because many older subjects have concomitant peripheral ARHL and age-related cognitive changes. In the last two decades, the association between cognitive impairment and ARHL has received great attention. Peripheral ARHL has recently been defined as the modifiable risk factor with the greatest impact on the development of dementia. Even if very few studies have analyzed the relationship between cognitive decline and age-related CAPD, a strong association was highlighted. Therefore, age-related CAPD could be a specific process related to neurodegeneration. Since these two disorders can be concomitant, drawing causal inferences is difficult. The assumption that ARHL, particularly age-related CAPD, may increase the risk of cognitive impairment in the elderly remains unchallenged. This review aims to summarize the evidence of associations between age-related CAPD and cognitive disorders and to define the diagnostic procedure of CAPD in the elderly. Finally, we highlight the importance of tailoring the rehabilitation strategy to this relationship. Future longitudinal studies with larger sample sizes and the use of adequate assessment tools that can disentangle cognitive dysfunction from sensory impairments are warranted.