Composite superparamagnetic colloidal suspensions assemble into a variety of higher-order structures when exposed to complex magnetic fields. These magnetic fields vary their direction, strength, or both as a function of time and can have additional dynamical aspects. As a result of the time-varying nature of the complex fields, the assembled structures undergo rotational dynamics. This thesis studies how complex fields modify the morphology of the assemblies and tune the dipolar interactions during rotational actuation. After an extensive review, the first part of the thesis elucidates the deformation of semiflexible DNA-linked superparamagnetic chains undergoing rotational motion under low-frequency circular and eccentric rotating fields. The chain deforms via transient coiling dynamics or steady-state periodic buckling that depend on the evolution of the dipolar interactions over time. In the second part, clusters and dimers of these colloids are studied under a high-frequency alternating rotating field. The inhibited rotation of the clusters coincides with the acquisition of anisotropic shapes. Novel dipolar interactions are uncovered upon analyzing the dynamics of dimers under this field, arising from a delay in the rotational dynamics of the colloids’ magnetization. Overall, this thesis describes how complex fields can be used to externally control the configurations of actuated superparamagnetic colloidal systems.