Electric and magnetic fields have enabled both technological applications and fundamental discoveries in the areas of bottom-up material synthesis, dynamic phase transitions, and biophysics of living matter. Electric and magnetic fields are versatile external sources of energy that power the assembly and self-propulsion of colloidal particles. In this Invited Feature Article, we classify the mechanisms by which external fields impact the structure and dynamics in colloidal dispersions and augment their nonequilibrium behavior. The paper is purposely intended to highlight the similarities between electrically and magnetically actuated phenomena, providing a brief treatment of the origin of the two fields to understand the intrinsic analogies and differences. We survey the progress made in the static and dynamic assembly of colloids and the self-propulsion of active particles. Recent reports of assembly-driven propulsion and propulsion-driven assembly have blurred the conceptual boundaries and suggest an evolution in the research of nonequilibrium colloidal materials. We highlight the emergence of colloids powered by external fields as model systems to understand living matter and provide a perspective on future challenges in the area of field-induced colloidal phenomena.