2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120496We classify six-dimensional homogeneous nearly Kähler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly Kähler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. The only four examples in dimension 6 are $S^3 \times S^3$, the complex projective space $\CM P^3$, the flag manifold $\mathbb F^3$ and the sphere $S^6$. We develop, about each of these spaces, a distinct aspect of nearly Kähler geometry and make in the same time a sharp description of its specific homogeneous structure.This is the english version of an older article written in french (Classification des variétés approximativement kähleriennes homogènes, Ann. Global Anal. Geom. 27, 201-225, 2005). It contains no new results. However, we modified the structure of the paper, simplified some proofs and added a lot of explanations, especially on 3-symmetric spaces. It can be read as a sort of survey on nearly Kähler manifoldsDifferential Geometry53C10, 53C15, 53C25, 53C28, 53C30text