Within the standard three-neutrino framework, the absolute neutrino masses and their ordering (either normal, NO, or inverted, IO) are currently unknown. However, the combination of current data coming from oscillation experiments, neutrinoless double beta (0νββ) decay searches, and cosmological surveys, can provide interesting constraints for such unknowns in the sub-eV mass range, down to O(10-1)  eV in some cases. We discuss current limits on absolute neutrino mass observables by performing a global data analysis that includes the latest results from oscillation experiments, 0νββ decay bounds from the KamLAND-Zen experiment, and constraints from representative combinations of Planck measurements and other cosmological data sets. In general, NO appears to be somewhat favored with respect to IO at the level of ∼2σ, mainly by neutrino oscillation data (especially atmospheric), corroborated by cosmological data in some cases. Detailed constraints are obtained via the χ2 method, by expanding the parameter space either around separate minima in NO and IO or around the absolute minimum in any ordering. Implications for upcoming oscillation and nonoscillation neutrino experiments, including β-decay searches, are also discussed.