The observational study of stellar magnetic fields is important for understanding not only the origin of such fields but also the impact they have on stellar evolution, through their influence on various transport processes occurring within or in the immediate surroundings of hot and cool stars. After drawing a broad panorama of the most challenging problems yet to be solved in this field, I propose a number of observing programs to progress significantly along these tracks and demonstrate that a VLT next generation instrument, consisting of a high-sensitivity and high-resolution dual-arm spectropolarimeter working at both optical and near-infrared wavelengths, would be the most efficient and appropriate facility worldwide for this research.