Layered copper-oxide superconductors exhibit the highest critical transition temperatures of any materials. Yet all of the known double perovskites A′A″B′B″O6 containing copper have a random or rock salt distribution of the B cations with the exception of the unique layered arrangement found in La2CuSnO6. Only the layered arrangement contains the CuO2
2- planes which are necessary for high-temperature superconductivity. The occurrence of layered or two dimensional structures increases markedly when vacancies are introduced on the oxygen sublattice, as evidenced in Ln
(Ln = lanthanide, Y: AE = Ba, Ca: 2 ≤ m ≤ 4). Similarities among oxygen-deficient structures, especially those with two-dimensional solid-state features, are discussed. Combined conductivity and thermopower analysis are presented to elucidate their unique internal chemistry, defect structure, and conduction parameters. In particular, data for La2-xSrxCuSnO6 are presented and related to the crystal chemistry of the copper-oxygen layer. These data are compared with La2Ba2Cu2Sn2O11 and La2Ba2Cu2Ti2O11 to illustrate the significance of oxygen vacancies on the properties of the copper oxygen planes. New layered cuprates are discussed including the mixed A-site stoichiometries Ln′Ln″AEm
(Ln = lanthanide, Y: AE = Ba, Ca: 2 ≤ m ≤ 4) which contain the smaller lanthanide (Ln″) ordered between the closely spaced, facing sheets of Cu-O square pyramids.