Aerosols interact with radiation and clouds. Substantial progress made over the past 40 years in observing, understanding, and modeling these processes helped quantify the imbalance in the Earth's radiation budget caused by anthropogenic aerosols, called aerosol radiative forcing, but uncertainties remain large. This review provides a new range of aerosol radiative forcing over the industrial era based on multiple, traceable, and arguable lines of evidence, including modeling approaches, theoretical considerations, and observations. Improved understanding of aerosol absorption and the causes of trends in surface radiative fluxes constrain the forcing from aerosol-radiation interactions. A robust theoretical foundation and convincing evidence constrain the forcing caused by aerosol-driven increases in liquid cloud droplet number concentration. However, the influence of anthropogenic aerosols on cloud liquid water content and cloud fraction is less clear, and the influence on mixed-phase and ice clouds remains poorly constrained. Observed changes in surface temperature and radiative fluxes provide additional constraints. These multiple lines of evidence lead to a 68% confidence interval for the total aerosol effective radiative forcing of -1.6 to -0.6Wm(-2), or -2.0 to -0.4Wm(-2) with a 90% likelihood. Those intervals are of similar width to the last Intergovernmental Panel on Climate Change assessment but shifted toward more negative values. The uncertainty will narrow in the future by continuing to critically combine multiple lines of evidence, especially those addressing industrial-era changes in aerosol sources and aerosol effects on liquid cloud amount and on ice clouds.