Four years after the discovery of superconductivity at high temperature in the Ba-La-Cu-O system, more than thirty new compounds have been synthesized, which can be classified in six series of copper oxides: La2CuO4 - type oxides, bismuth cuprates, YBa2Cu3O7 family, thallium cuprates, lead cuprates and Nd2CuO4 - type oxides. Despite their quite different specific natures, close relationships allow their structures to be simply described through a single mechanism. The fifth first families can indeed be described as intergrowths of multiple oxygen deficient perovskite slabs with multiple rock salt-type slabs, according to the representation [ACuO3-x]m [AO]n.The n and m values are integer in the parent structures, n varying from 0 to 3 and m from 1 to 4; every member of this large family can thus be symbolized by [m,n]. The oxygen deficient character of the perovskite slabs involves the existence or the co-existence of several types of copper environment: octahedral, pyramidal and square planar.Both mechanisms, oxygen deficiency and intergrowth, are well known to give rise easily to nonstoichiometry phenomena. Numerous and various phenomena have actually been characterized in these cuprates, strongly depending on the thermal history of the samples.