In this review we will focus on how magnetic fields can be used to manipulate the motion of various micro- and nanostructures in solution. We will distinguish between ferromagnetic, paramagnetic and diamagnetic materials. Furthermore, the use of various kinds of magnetic fields, such as homogeneous, inhomogeneous and rotating magnetic fields, is discussed. To date most research has focused on the use of ferro- and paramagnetic materials, but here we also describe the possibilities of magnetic manipulation of diamagnetic materials. Since the vast majority of soft matter is diamagnetic, this paves the way for many new applications to manipulate the motion of micro- and nanostructures.