A complete literature review, critical evaluation, and thermodynamic optimization of phase equilibrium and thermodynamic properties of all available oxide phases in the MnO-B2O3 and MnO-B2O3-SiO2 systems at 1 bar pressure are presented. Due to the lack of the experimental data in these systems, the systematic trend of CaO- and MgO-containing systems were taken into account in the optimization. The molten oxide phase is described by the Modified Quasichemical Model. A set of optimized model parameters of all phases is obtained which reproduces all available and reliable thermodynamic and phase equilibrium data. The unexplored binary and ternary phase diagrams of the MnO-B2O3 and MnO-B2O3-SiO2 systems have been predicted for the first time. The thermodynamic calculations relevant to the oxidation of advanced high-strength steels containing boron were performed to find that B can form liquid B2O3-SiO2-rich phase in the annealing furnace under reducing N2-H2 atmosphere, which can significantly influence the wetting behavior of liquid Zn in Zn galvanizing process.