Objectives: Sleep is associated with cognitive function in older adults. In the current study, we examined this relationship from subjective and objective perspectives, and determined the robustness and dimensional specificity of the associations using a comprehensive modelling approach. Methods: Multiple dimensions of subjective (sleep quality and daytime sleepiness) and objective sleep (sleep stages, sleep parameters, sleep spindles, and slow oscillations), as well as subjectively reported and objectively measured cognitive function were collected from 55 older adults. Specification curve analysis was used to examine the robustness of correlations for the effects of sleep on cognitive function. Results: Robust associations were found between sleep and objectively measured cognitive function, but not with subjective cognitive complaints. In addition, subjective sleep showed robust and consistent associations with global cognitive function, whereas objective sleep showed a more domain-specific association with episodic memory. Specifically, subjective sleep quality and daytime sleepiness correlated with global cognitive function, and objective sleep parameters correlated with episodic memory. Conclusions: Overall, associations between sleep and cognitive function in older adults depend on how they are measured and which specific dimensions of sleep and domains of cognitive function are considered. It highlights the importance of focusing on specific associations to ameliorate the detrimental effects of sleep disturbance on cognitive function in later life.