Evapotranspiration (ET) is critical in linking global water, carbon and energy cycles. However, direct measurement of global terrestrial ET is not feasible. Here, we first reviewed the basic theory and state-of-the-art approaches for estimating global terrestrial ET, including remote-sensingbased physical models, machine-learning algorithms and land surface models (LSMs). We then utilized 4 remotesensing-based physical models, 2 machine-learning algorithms and 14 LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the ensemble means of annual global terrestrial ET estimated by these three categories of approaches agreed well, with values ranging from 589.6 mm yr-1 (6.56 × 104 km3 yr-1) to 617.1 mm yr-1 (6.87 × 104 km3 yr-1). For the period from 1982 to 2011, both the ensembles of remote-sensing-based physical models and machine-learning algorithms suggested increasing trends in global terrestrial ET (0.62 mm yr-2 with a significance level of p < 0.05 and 0.38 mm yr-2 with a significance level of p < 0.05, respectively). In contrast, the ensemble mean of the LSMs showed no statistically significant change (0.23 mm yr-2, p > 0.05), although many of the individual LSMs reproduced an increasing trend. Nevertheless, all 20 models used in this study showed that anthropogenic Earth greening had a positive role in increasing terrestrial ET. The concurrent small interannual variability, i.e., relative stability, found in all estimates of global terrestrial ET, suggests that a potential planetary boundary exists in regulating global terrestrial ET, with the value of this boundary being around 600 mm yr-1. Uncertainties among approaches were identified in specific regions, particularly in the Amazon Basin and arid/semiarid regions. Improvements in parameterizing water stress and canopy dynamics, the utilization of new available satellite retrievals and deep-learning methods, and model-data fusion will advance our predictive understanding of global terrestrial ET.