Studies of neuropathology-cognition associations are not common and have been limited by small sample sizes, long intervals between autopsy and cognitive testing, and lack of breadth of neuropathology and cognition variables. This study examined domain-specific effects of common neuropathologies on cognition using data (N = 652) from two large cohort studies of older adults. We first identified dimensions of a battery of 17 neuropsychological tests, and regional measures of Alzheimer's disease (AD) neuropathology. We then evaluated how cognitive factors were related to dimensions of AD and additional measures of cerebrovascular and Lewy Body disease, and also examined independent effects of brain weight. All cognitive domains had multiple neuropathology determinants that differed by domain. Neocortical neurofibrillary tangles were the strongest predictors of most domains, while medial temporal tangles showed a weaker relationship with episodic memory. Neuritic plaques had relatively strong effects on multiple domains. Lewy bodies and macroscopic infarcts were associated with all domains, while microscopic infarcts had more limited associations. Brain weight was related to all domains independent of specific neuropathologies. Results show that cognition is complexly determined by multiple disease substrates. Neuropathological variables and brain weight contributed approximately a third to half of the explained variance in different cognitive domains.