In this talk, we will present our recent results on the classification of homogeneous Finsler spaces with positive flag curvature. In particular, we give the complete lists of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. In the even-dimensional case, we are able to give a complete list of homogeneous Finsler spaces which admit invariant Finsler metrics with positive flag curvature. However, in the odd-dimensional case, we only get some partial results.