  The structure of nearly K\"ahler manifolds was studied by Gray in several
papers. More recently, a relevant progress on the subject has been done by
Nagy. Among other results, he proved that a strict and complete nearly K\"ahler
manifold is locally a Riemannian product of homogeneous nearly K\"ahler spaces,
twistor spaces over quaternionic K{\"ahler manifolds and six-dimensional nearly
K\"ahler manifolds, where the homogeneous nearly K\"ahler factors are also
3-symmetric spaces. In the present paper, using the lists of $3$-symmetric
spaces given by Wolf & Gray, we display the exhaustive list of irreducible
simply connected homogeneous strict nearly K\"ahler manifolds. For such
manifolds, we give details relative to the intrinsic torsion and the Riemannian
curvature. Additionally, we determine the canonical fibration for those with
special algebraic torsion.
