Cobalt surface oxides where grown on Pt(111) by depositing Co and dosing with molecular oxygen at temperatures ranging between 300 K and 740 K. Oxidation of 1 monolayer (ML) Co results in a two-dimensional (2D) moiré structure, observed both using low energy electron diffraction and scanning tunneling microscopy, and interpreted as a polar (oxygen terminated) CoO(111) atomic bilayer. With respect to bulk CoO, it is expanded by 2.7±0.5% in the surface plane. An almost flawless moiré pattern is obtained after a final step of annealing at 740 K in oxygen. Insufficient oxidation leads to defects in the moiré pattern, consisting of triangular dislocation loops of different sizes; the smaller ones occupying one half of the moiré cell. Low-temperature annealing (450 K) can be used to create a zigzag phase, which is mainly observed in 1-ML thick areas after several cycles of Co deposition (1 ML each) and oxidation at 10 -7 mbar. The CoO films obtained by deposition/oxidation cycles exhibit Stranski-Krastanov growth; the structure of the 2D layer in between the islands depending on the thermal treatment. After annealing at 740 K it exhibits the moiré pattern, while the zigzag phase was observed after low-temperature annealing. The second monolayer consists of a moiré pattern different from that of the 1st layer, presumably a wurtzite-like structure. Above the 3rd layer, we observe only small 3D islands, which exhibit a band gap. We have also studied oxidation of surface alloys obtained by depositing Co and annealing. On these surfaces, we found a quasi-(3×3) reconstruction. Structure models are presented for all phases observed, and we argue that some of the moiré-like structures might be useful as templates for metal cluster growth.