By reviewing the experimental and theoretical literature on γ′‐Fe4N, and by a systematic survey of predictions by the LDA, PBE, WC, LDA + U (2×), PBE + U (2×) and B3PW91 exchange‐correlation functionals, the structural, magnetic and hyperfine properties of this material as well as their pressure dependencies are interpreted. The hypothesis is put forward that γ′‐Fe4N as found in Nature is exactly at a steep transition between low‐spin and high‐spin behaviour. PBE + U (U = 0.4 eV) is identified as the most accurate exchange‐correlation functional for this material, although it is needed to fix the magnetization at the experimental value to obtain a satisfying description. Remaining disagreement between theory and experiment is pointed out. A recent experimental claim for a giant magnetic moment in γ′‐Fe4N is discussed, and is not reproduced by our calculations. We expect that the new insight obtained in the present work can lead to a consistent ab initio modeling of other materials in the iron‐nitrogen binary system. In an accompanying didactic section, the physics behind some common exchange‐correlation functionals is outlined. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)