The phase relations in rare earth-Mn-O systems in air are considered. Most of the phase diagrams of these systems fall into two distinct groups: R'-Mn-O (R'= Y, Ho-Lu) and R"-Mn-O (R" = Pr, Nd, Sm-Dy). In addition, the Sc-Mn-O, La-Mn-O, and Ce-Mn-O systems have phase-diagram features of their own. The Ce-Mn-O system contains no ternary oxides or solid solutions: there are only mixtures of cerium and manganese oxides. The Sc-Mn-O system has phase-diagram features in common with both the R'-Mn-O and M-Mn-O (M = Mg, Al, 3d transition metal) systems. The La-Mn-O phase diagram can be thought of as a deoenerate diacyram of the R"-Mn-O erroup, since (LaMnO5)-O-2 exists at oxygen pressures higher than atmospheric pressure. The R'-Mn-O and R"-Mn-O systems contain two chemical compounds, RMnO3 and RMn2O5, but differ in the crystal structure of RMnO3: hexagonal in the R' group and orthorhombic perovskite-like in the R" group. A key role in determining the structure of RMnO3 is played by the size factor. In both groups, the RMn2O5 compounds dissociate in air by the reaction RMn2O5 = RMnO3 + 1/3 RMn3O4 + 1/3 O-2. The dissociation temperature of RMn2O5 is shown to correlate with the atomic number of R, the total number of 4f electrons, the number of unpaired 4f electrons, and the ionic radius of R3+.