Atmospheric aerosols affect the Earth's climate in many ways, including acting as the seeds on which cloud droplets form. Since a large fraction of these particles is anthropogenic, the clouds' microphysical and radiative characteristics are influenced by human activity on a global scale leading to important climatic effects. The respective change in the energy budget at the top of the atmosphere is defined as the effective radiative forcing due to aerosol-cloud interaction (ERFaci). It is estimated that the ERFaci offsets presently nearly 1/4 of the greenhouse-induced warming, but the uncertainty is within a factor of two. A common method to calculate the ERFaci is by the multiplication of the susceptibility of the cloud radiative effect to changes in aerosols by the anthropogenic change of the aerosol concentration. This has to be done by integrating it over all cloud regimes. Here we review the various methods of the ERFaci estimation. Global measurements require satellites' global coverage. The challenge of quantifying aerosol amounts in cloudy atmospheres are met with the rapid development of novel methodologies reviewed here. The aerosol characteristics can be retrieved from space based on their optical properties, including polarization. The concentrations of the aerosols that serve as cloud drop condensation nuclei can be also estimated from their impact on the satellite-retrieved cloud drop number concentrations. These observations are critical for reducing the uncertainty in the ERFaci calculated from global climate models (GCMs), but further development is required to allow GCMs to properly simulate and benefit these novel observables.