The current standard of electronic devices and data storage media has reached a level such that magnetic materials have to be fabricated on a nanometer scale. In particular, the emerging concept of spintronics, which is based on fact that current carriers have not only charge but also spin, requires the assembling of nanometer-sized magnetic structures with desired magnetic properties. It is this background that motivates scientists and engineers to attempt to grow and characterize magnetic objects at smaller and smaller length scales, from 2D films and multilayers to 1D wires and eventually to 0D dots. In this article, some of the most significant progress in recent years in the effort of growing artificially structured magnetic materials are reviewed. The new structural and magnetic properties of these materials are discussed, with an emphasis on the correlation between structure and magnetism, which also serves as guidance for improving their magnetic properties. The emerging emphasis is on converting the existing knowledge into growing and studying low-dimensional complex materials, which promise to have considerably higher "tuning´´ ability for desired properties.