In certain alloy systems, a liquid of a fixed composition freezes to form a mixture of two solid phases, one of which may be faceted and the other nonfaceted (i.e., a ‘degenerate’ or irregular eutectic). The role of trace metallic additions on the microstructure of the eutectic has received significant research interest over the last half-century, culminating in advances in theoretical, computational, and experimental fronts. The drastic morphological, topological, and crystallographic changes that accompany metallic additions strongly influence the mechanical properties of the as-synthesized eutectic microstructure. In this review, we survey the mechanistic origins leading to a modified eutectic microstructure and describe the current status in the field of eutectic solidification in the presence of metallic modifying agents. We will also discuss the remaining challenges and future opportunities that would help move the field forward and enable bottom–up tuning of the complex degenerate microstructures to technological demands.