I will report on a joint work in progress with Andreas Kollross, in which we are extending the classification of isometric cohomogeneity-one actions on irreducible symmetric spaces of compact type obtained by Kollross in 1998 to the general reducible case. In order to do so, we first obtain an explicit classification of isometric transitive actions on the aforementioned (reducible) spaces up to subgroup-conjugacy by using the works of Onishchik on decompositions of simple compact Lie algebras. I will restrict to the (less convoluted) case when all the de Rham factors are of non-group type and make comments on the general case.