To achieve climate stabilization, substantial emission reductions are needed. Emissions from industrial point sources can be reduced by applying carbon capture and storage (CCS) methods, which capture carbon dioxide (CO₂) before it is released to the atmosphere. CCS applications typically target CO₂ storage within geological reservoirs. Accelerated weathering of limestone (AWL) provides an alternative CCS approach, in which CO₂ is stored as dissolved inorganic carbon in the ocean. At present, AWL technology remains at the pilot scale with no industrial implementation. Here, we review the proposed reactor designs for AWL, comparing them in terms of CO₂ capture efficiency, CaCO₃ dissolution efficiency, CO₂ sequestration efficiency, and water usage. For this, we represent AWL as a four step process: (i) CO₂ dissolution, (ii) CaCO₃ dissolution, (iii) alkalinization (step only included in the case of buffered AWL), and lastly (iv) re-equilibration. AWL application is generally characterized by a large water usage and the need for large reactor sizes. Unbuffered AWL approaches show substantial degassing of CO₂ back to the atmosphere after the process water is discharged. Buffered AWL compensates the unreacted CO₂ by Ca(OH)₂ addition, and hence prevents degassing, which substantially increases the CO₂ sequestration efficiency. Yet, buffered AWL require a source of  CO₂-neutral Ca(OH)₂. The need for process water can be reduced by increasing the CO₂ fraction of the gas stream or increasing its pressure. Further optimization of the pulverized carbonate particles could reduce the amount of Ca(OH)₂ needed to buffer the unreacted CO₂. The anticipated CO₂ sequestration efficiency of buffered AWL is comparable with that projected for large-scale CCS in geological reservoirs.