  We classify six-dimensional homogeneous nearly K\"{a}hler manifolds and give
a positive answer to Gray and Wolf's conjecture: every homogeneous nearly
K\"{a}hler 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 K\"{a}hler geometry and make in the same time a sharp
description of its specific homogeneous structure.
