The primary criterion for nanostructures to be assembled under the influence of a magnetic field is that, obviously, the nanostructures should be responsive to magnetic forces. Thus, magnetic nanoparticles such as Fe3O4, Ni and Co, or hybrid nanoparticles with a magnetic component can be directed by magnetic fields towards self-assemblies with much ease, Figure (a). As shown by Singh et al. in Figure (b), by applying an external magnetic field, a self-assembled monolayer of nanoparticles over diethylene glycol can be turned into an array of helical superstructures by the interplay of van der Waals and magnetic dipole-dipole interactions, Zeeman coupling, and entropic forces. Taheri et al. demonstrated a similar approach for the self-assembly of iron oxide nanoparticles induced by an external magnetic field to form 1D nano-chains, monolayer sheets in 2D, and large 3D cuboids with internal ordering. The self-assembly of the nanocubes can be elucidated considering the dipole-dipole interaction of small superparamagnetic particles. The importance of this work stems from the fact that the assembled iron oxide nanocubes are very small (~8.2 nm), which demonstrates the feasibility of the magnetic field directed self-assembly method even for such small nanostructures. Linear structures of magnetic nanoparticles are also interesting for various applications, as will be discussed later in the application section. Chong et al. showed the linear assembly of Fe3O4 nanoparticles and their protection by a silica shell that makes the assemblies mechanically robust and chemically resistant, Figure ). Another approach towards microscopic control of nanostructure assemblies by an external magnetic field is by microscopic variation of the magnetic field. As shown in Figure (d), Demirörs et al. showed that periodic (periodicity 10 micron) magnetic moulds with Ni (~2 micron) islands over PDMS can selectively assemble magnetic microparticles with high efficiency (fidelity of the assembly ~97 %). A similar approach can be implemented with smaller magnetic nanoparticles for nanoscale assemblies in desired applications. As demonstrated by Erb et al., application of a magnetic field on a colloidal mixture of diamagnetic and paramagnetic particles in a magnetized ferrofluid results in the spontaneous formation of fractal clusters, Figure ). While the particles in this work are of mm sizes, a similar phenomenon at nanoscale with nanoparticles remains as an interesting aspect to be investigated in the future. The primary advantage of magnetic field directed self-assembly is that the external field can be easily modulated to control the assembled structure. Also, in many applications, hybrid nanoparticles with a magnetic component can be easily separated after a process simply by a magnetic field. nanocubes assembled on the DEG surface. Reprinted with permission ©2014, AAAS. Magneticfield-induced self-assembled 3D cuboid which consists of more than 10,000 iron oxide nanocubes. Reprinted with permission © 2015, National Academy of Sciences. (c) Magnetic-field-induced linear assembly of Fe3O4 nanoparticles and protection by silica shell for stability. Reprinted with permission © 2013 John Wiley & Sons. (d) Magnetic moulds with Ni and PDMS islands for variable magnetic field for directed assembly of particles (top), 2.85 mm magnetic particles in size assembled on a square grid of nickel islands (middle), 1.2 mm diamagnetic particles arrange in the PDMS voids of a hexagonal grid of nickel rings. Reprinted with permission © 2013 Nature Publishing Group. (e,f) Rotationally symmetric fractal clusters form from non-magnetic particles (red and green) and paramagnetic core particles by the application of a magnetic field. Reprinted with permission © 2009 Nature publishing group.