Research progress on understanding magnetic steel core losses is presented in this report. Three major aspects have been thoroughly investigated: 1, experimental characterization of core losses, 2, fundamental physical understanding of core losses and development of core loss formulas, and 3, design of more efficient machine based on the new formulations. Considerable progress has been achieved during the four years of research and the main achievements are summarized in the following:For the experimental characterization, a specially designed advanced commercial test bench was commissioned in addition to the development of a laboratory system with advanced capabilities. The measured properties are core losses at low and higher frequencies, with sinusoidal and non-sinusoidal excitations, at different temperatures, with different measurement apparatus (Toroids, Epstein etc).An engineering-based core loss formula has been developed which considers skin effect. The formula can predict core losses for both sinusoidal and non-sinusoidal flux densities and frequencies up to 4000 Hz. The formula is further tested in electric machines. The formula error range is 1.1% -7.6% while the standard formulas can have % errors between -8.5% -+44.7%.Two general core loss formulas, valid for different frequencies and thickness, have been developed by analytically and numerically solving Maxwell's equations based on a physical investigation of the dynamic hysteresis effects of magnetic materials. To our knowledge, they are the first models that can offer accurate core loss prediction over a wide range of operating frequencies and lamination thicknesses without a massive experimental database of core losses.The engineering core loss formula has been used with commercial software. The formula performs better than the modified Steinmetz and Bertotti's model used in Cedrat/Magsoft Flux 2D/3D. The new formula shows good correlation with measured results under both sinusoidal and non-sinusoidal excitations.