Abstract: An almost Hermitian manifold is said to be nearly Kähler if the covariant derivative of its almost complex structure is totally skew-symmetric. In dimension six, these spaces are of particular interest, as the Riemannian cone of a six-dimensional strict nearly Kähler manifold (except for the sphere \(\mathsf{S}^6\)) has special holonomy \(\mathsf{G}_2\). It was shown by Butruille that the simply connected homogeneous strict nearly Kähler manifolds of dimension six are \(\mathsf{S}^6\), the flag manifold \(\mathsf{F}(\mathbb{C}^3)\), the complex projective space \(\mathbb{C}\mathsf{P}^3\) and the almost product \(\mathsf{S}^3\times \mathsf{S}^3\). In this talk, I will report on a joint work with Alberto Rodríguez Vázquez (Université Libre de Bruxelles, Belgium) in which we classify the totally geodesic submanifolds of the (non-symmetric) homogeneous nearly Kähler 6-manifolds, as well as their \(\mathsf{G}_2\)-cones. To this end, we develop the tools to attack the problem in (naturally reductive) homogeneous spaces and Riemannian cones.