Transition metal oxides offer large opportunities to study relationships between structures and properties. Indeed these compounds crystalline in numerous frameworks corresponding to different dimensionalities and, accordingly, show a huge variety of properties (as high Tc superconductivity, colossal magnetoresistivity, multiferroicity..). The control of the oxidation state of the transition metal, via the monitoring of the oxygen content, is of prime importance to understand and optimize the properties, due to the strong coupling that exists between the lattice and the charges and spins of the transition metals. In this large playground for chemists, we reinvestigated several 2D-compounds derived from delafossite structure. Considering this paper as a very short review, we report here the results obtained on CuMO2 compounds (with M = Cr, Mn or Mn+Cu) by using a combination of techniques, as X-ray, neutrons and/or electrons diffraction on poly-crystals for structural characterisations that are correlated with electrical and/or magnetic properties. The complementarity of studies is also addressed by the synthesis and characterization of single crystals in addition to poly-crystals. Moreover the comparison of the structures of similar Cr and Mn based oxides highlights the crucial role of the Jahn-Teller effect of trivalent manganese to lift the degeneracy, which is responsible of the magnetic frustration in CuCrO2.