There is currently little consensus regarding what must be explained by theories of cognitive aging. In the present article, four empirical generalizations that seem to imply certain constraints in theorizing are identified. These generalizations, and their possible implications or constraints, are that (1) age-related differences are found in a wide range of cognitive variables, implying that either a large number of specific factors or a small number of general factors must be contributing to the age-related differences; (2) the age-related influences on different cognitive variables are not independent, and unique age-related influences appear to be few in number and small in magnitude, implying that some fairly general factors need to be postulated to account for the shared age-related influences; (3) only a small proportion of distinct age-related variance occurs late in practice and at long presentation durations, implying that adequate explanations must include factors operating when the individuals are just beginning to perform the task and when the stimuli can first be registered; and (4) measures of how quickly very simple cognitive tasks can be performed share considerable age-related variance with many cognitive variables, implying that factors related to simple processing efficiency need to be incorporated into the explanations.