The article discusses the use of magnetic bremsstrahlung at short radio wavelengths for measuring solar magnetic fields. The polarization and brightness spectra observed at millimeter wavelengths can be used to deduce the vertical component of the chromospheric magnetic field both in the quit Sun and in active regions. State-of-the-art three-dimensional (3D) radiative magnetohydrodynamic (R-MHD) simulations of the quiet solar atmosphere were used to synthesize observational deliverables at the wavelengths of the Atacama Large Millimeter/Submillimeter Array (ALMA) and to test the applicability of the method. The article provides selected observational examples of the successful application of the method and presents an overview of the recent developments and potential of the magnetic field measurements with ALMA.