Epitaxial cobalt oxide films on Ir(100) exhibit a rich scenario of different structural phases which are reviewed in this paper. The great majority of phases could be, as a rare case, crystallographically described by the joint application of atomically resolved STM and quantitative LEED, whereby structural surprises were more the rule than the exception. So, the oxide grows in the polar (111) orientation for both the Co3O4 and CoO stoichiometry on the bare Ir substrate in spite of the latter's square symmetry. Moreover, the film orientation can be tuned to non-polar (100) growth when one or several pseudomorphic Co layers are introduced as an interface between oxide and Ir substrate. By using the nanostructured Ir(100)-(5 × 1)-H phase as a template a nanostructured Co film can be formed whose oxidation leads to a nanostructured oxide. The nominally polar films circumvent the polarity problem by appropriate surface terminations. That of CoO(111) is, again as a surprise, realized by a switch from rocksalt-type to wurtzite-type stacking near the surface, by which the latter becomes metallic. The stepwise oxidation of a pseudomorphic Co layer on the bare Ir substrate leads to the sequential formation of rocksalt-type tetrahedral Co-O building blocks (with intermediate BN-type blocks) whereby the Co species more and more assume positions determined by the inner-oxidic binding.