The ocean holds vast quantities of carbon that it continually exchanges with the atmosphere through the air-sea interface. Because of its enormous size and relatively rapid exchange of carbon with the atmosphere, the ocean controls atmospheric CO2 concentration and thereby Earth’s climate on timescales of tens to thousands of years. This review examines the basic functions of the ocean’s carbon cycle, demonstrating that the ocean carbon inventory is determined primarily by the mass of the ocean, by the chemical speciation of CO2 in seawater, and by the action of the solubility and biological pumps that draw carbon into the ocean’s deeper layers, where it can be sequestered for decades to millennia. The ocean also plays a critical role in moderating the impacts of climate change by absorbing an amount of carbon equivalent to about 25% of anthropogenic CO2 emissions over the past several decades. However, this also leads to ocean acidification and reduces the chemical buffering capacity of the ocean and its future ability to take up CO2. This review closes with a look at the uncertain future of the ocean carbon cycle and the scientific challenges that this uncertainty brings.