“…Among those spaces, there are three homogeneous Riemannian manifolds: R 3 , where the classical theory of minimal surfaces has been developed, and S 2 × R and H 2 × R, where many authors have been actively working. Giving a complete list of references on the subject is far from being possible so we will only mention a few of them: Nelli and Rosenberg [12] proved a Jenkins-Serrin-type theorem in H 2 ×R, Hauswirth [6] constructed minimal examples of Riemann type, Sá Earp and Tobiana [18] investigated the screw motion invariant surfaces in H 2 ×R, Daniel [4] and Hauwirth, Sá Earp and Tobiana [7] showed, independently, the existence of an associated family of minimal immersions for simply connected minimal surfaces in S 2 ×R and H 2 ×R, Urbano and the author [20] tackled a general study of minimal surfaces in S 2 × S 2 with applications to S 2 × R, very recently Manzano, Plehnert and the author [9] constructed orientable and non-orientable even Euler characteristic embedded minimal surfaces in the quotient S 2 × S 1 and Martín, Mazzeo and Rogríguez [10] constructed the first examples of complete, properly embedded minimal surfaces in H 2 × R with finite total curvature and positive genus.…”