The late Oligocene and early Miocene periods, some 21 to 27 million years ago, have generally been viewed as times of moderate global warmth and ice-free conditions. Yet several lines of evidence suggest that this interval was punctuated by at least one, and possibly several, episodes of high-latitude cooling and continental glaciation(1-3). Here, we present stable-isotope and per cent coarse-fraction data from an equatorial, western Atlantic deep-sea-sediment core that provide high-resolution records of the climate variability across the Oligocene/Miocene transition (22.5-25.7 million years ago), A strong 40-kyr periodicity in the oxygen isotope record is consistent with a high-latitude orbital (obliquity) control on ice-volume and temperature. Orbital influences are also apparent at precession and eccentricity frequencies, including a series of similar to 400-kyr oscillations that culminate in distinct maxima at the Oligocene/Miocene boundary, about 23.7 million years ago. Covariance between the carbon and oxygen isotope records suggests that the oceanic carbon cycle may have contributed to global cooling during the similar to 400-kyr cycles, particularly at the Oligocene/Miocene boundary.