1) Accelerated weathering of limestone has the potential to store large volumes of carbon dioxide by increasing alkalinity in the oceans, but questions remain about environmental impacts and stability of stored carbon. 2) Laboratory experiments and geochemical modeling show that limestone dissolution rates and carbon dioxide uptake can be modeled and are dependent on factors like surface area, water volume, temperature, and gas-liquid interface. 3) At an industrial scale, accelerated weathering of limestone would require very large reactor volumes, on the order of 105-106 m3, to sequester a million tons of carbon dioxide per year.