The potential of nanotechnology in the biomedical field has been crucial for contributing to the possibility of efficiently meeting present necessities with novel materials. Over the last few decades, nanostructures with a core/shell structure have attracted significant attention because of the possibility of changing their physical properties by varying their chemistry and geometry. These structures have become relevant in targeted therapy (drug delivery and treatments to complement chemotherapy and radiotherapy), imaging and in the stimulation of cellular functions. Thus in this paper the current development of core/shell nanostructures is reviewed, emphasizing the physical properties of those that have been proposed as potentially having biomedical applications, which are based in a magnetic behavior or in a mixture of magnetic and electric (multiferroic) phenomena.