Parental age is increasing rapidly in many countries. Analysis of this potentially important influence on offspring well-being is hampered by strong secular trends and socioeconomic patterning and by a shortage of follow-up data for adult offspring. We used Swedish national data on up to 3,653,938 offspring to consider the associations of parental age with a suite of outcomes in adult offspring, comparing the results from an array of statistical methods for optimal causal inference. The offspring of older mothers had higher BMI, blood pressure, height, intelligence, non-cognitive ability and socioeconomic position. They were less likely to smoke or to be left-handed. Associations with paternal age were strongly, but not completely, attenuated by adjustment for maternal age. Estimates from the commonly-used sibling comparison method were driven primarily by a pathway mediated by offspring date of birth when outcomes showed strong secular trends. These results suggest that the intra-uterine and early life environments provided by older mothers may be detrimental to offspring cardiovascular health, but that their greater life experience and social position may bring intellectual and social advantages to their offspring. The analysis of parental age presents particular challenges, and further methodological developments are needed.