The Twomey effect describes the radiative forcing associated with a change in cloud albedo due to an increase in anthropogenic aerosol emissions. It is driven by the perturbation in cloud droplet number concentration (1Nd; ant) in liquid-water clouds and is currently understood to exert a cooling effect on climate. The Twomey effect is the key driver in the effective radiative forcing due to aerosol–cloud interactions, but rapid adjustments also contribute. These adjustments are essentially the responses of cloud fraction and liquid water path to 1Nd; ant and thus scale approximately with it. While the fundamental physics of the influence of added aerosol particles on the droplet concentration (Nd) is well described by established theory at the particle scale (micrometres), how this relationship is expressed at the large-scale (hundreds of kilometres) perturbation, 1Nd; ant, remains uncertain. The discrepancy between process understanding at particle scale and insufficient quantification at the climate-relevant large scale is caused by co-variability of aerosol particles and updraught velocity and by droplet sink processes. These operate at scales on the order of tens of metres at which only localised observations are available and at which no approach yet exists to quantify the anthropogenic perturbation. Different atmospheric models suggest diverse magnitudes of the Twomey effect even when applying the same anthropogenic aerosol emission perturbation. Thus, observational data are needed to quantify and constrain the Twomey effect. At the global scale, this means satellite data. There are four key uncertainties in determining 1Nd; ant, namely the quantification of (i) the cloud-active aerosol – the cloud condensation nuclei (CCN) concentrations at or above cloud base, (ii) Nd, (iii) the statistical approach for inferring the sensitivity of Nd to aerosol particles from the satellite data and (iv) uncertainty in the anthropogenic perturbation to CCN concentrations, which is not easily accessible from observational data. This review discusses deficiencies of current approaches for the different aspects of the problem and proposes several ways forward: in terms of CCN, retrievals of optical quantities such as aerosol optical depth suffer from a lack of vertical resolution, size and hygroscopicity information, non-direct relation to the concentration of aerosols, difficulty to quantify it within or below clouds, and the problem of insufficient sensitivity at low concentrations, in addition to retrieval errors. A future path forward can include utilising co-located polarimeter and lidar instruments, ideally including high-spectral-resolution lidar capability at two wavelengths to maximise vertically resolved size distribution information content. In terms of Nd, a key problem is the lack of operational retrievals of this quantity and the inaccuracy of the retrieval especially in broken-cloud regimes. As for the Nd-to-CCN sensitivity, key issues are the updraught distributions and the role of Nd sink processes, for which empirical assessments for specific cloud regimes are currently the best solutions. These considerations point to the conclusion that past studies using existing approaches have likely underestimated the true sensitivity and, thus, the radiative forcing due to the Twomey effect.