Two-dimensional materials, with their ultimate thinness, maximum surface area, and unique properties, become increasingly attractive for various device applications. We identify several novel iron and manganese two-dimensional compounds using density-functional-theory. Fe and Mn monochalcogenides are stable in an inverted-litharge structure with a low formation energy, which indicates that these materials can be synthesized by, e.g., chemical vapor deposition. Hybrid-density functional calculations predict that MnSe and MnTe are semiconductors, with indirect bandgaps of 2.6 and 2.1 eV, respectively. The band edge positions of both materials straddle the redox potentials of water, showing their potential as photocatalyst for water-splitting. We find that two-dimensional MnSb is magnetic and stable in a square lattice. Using a Heisenberg model we estimate that MnSb is a room temperature ferromagnetic metal. Our prediction can guide new experiment for the synthesis of these new twodimensional materials for potential applications in energy conversion devices.