Global aviation operations contribute to anthropogenic climate change via a complex set of processes that lead to a net surface warming. Of importance are aviation emissions of carbon dioxide (CO₂), nitrogen oxides (NO_x), water vapor, soot and sulfate aerosols, and increased cloudiness due to contrail formation. Aviation grew strongly over the past decades (1960-2018) in terms of activity, with revenue passenger kilometers increasing from 109 to 8269 billion km yr^-1, and in terms of climate change impacts, with CO₂ emissions increasing by a factor of 6.8 to 1034 Tg CO₂ yr^-1. Over the period 2013-2018, the growth rates in both terms show a marked increase. Here, we present a new comprehensive and quantitative approach for evaluating aviation climate forcing terms. Both radiative forcing (RF) and effective radiative forcing (ERF) terms and their sums are calculated for the years 2000-2018. Contrail cirrus, consisting of linear contrails and the cirrus cloudiness arising from them, yields the largest positive net (warming) ERF term followed by CO₂ and NO_x emissions. The formation and emission of sulfate aerosol yields a negative (cooling) term. The mean contrail cirrus ERF/RF ratio of 0.42 indicates that contrail cirrus is less effective in surface warming than other terms. For 2018 the net aviation ERF is +100.9 milliwatts (mW) m^-2 (5-95% likelihood range of (55, 145)) with major contributions from contrail cirrus (57.4 mW m^-2), CO₂ (34.3 mW m^-2), and NO_x (17.5 mW m^-2). Non-CO₂ terms sum to yield a net positive (warming) ERF that accounts for more than half (66%) of the aviation net ERF in 2018. Using normalization to aviation fuel use, the contribution of global aviation in 2011 was calculated to be 3.5 (4.0, 3.4) % of the net anthropogenic ERF of 2290 (1130, 3330) mW m^-2. Uncertainty distributions (5%, 95%) show that non-CO₂ forcing terms contribute about 8 times more than CO₂ to the uncertainty in the aviation net ERF in 2018. The best estimates of the ERFs from aviation aerosol-cloud interactions for soot and sulfate remain undetermined. CO₂-warming-equivalent emissions based on global warming potentials (GWP* method) indicate that aviation emissions are currently warming the climate at approximately three times the rate of that associated with aviation CO₂ emissions alone. CO₂ and NO_x aviation emissions and cloud effects remain a continued focus of anthropogenic climate change research and policy discussions.