Many metals have biological functions and play important roles in human health. Copper (Cu) is an essential metal that supports normal cellular physiology. Significant research efforts have focused on identifying the molecules and pathways involved in dietary Cu uptake in the digestive tract. The lack of an adequate in vitro model for assessing Cu transport processes in the gut has led to contradictory data and gaps in our understanding of the mechanisms involved in dietary Cu acquisition. The recent development of organoid technology has provided a tractable model system for assessing the detailed mechanistic processes involved in Cu utilization and transport in the context of nutrition. Enteroid (intestinal epithelial organoid)-based studies have identified new links between intestinal Cu metabolism and dietary fat processing. Evidence for a metabolic coupling between the dietary uptake of Cu and uptake of fat (which were previously thought to be independent) is a new and exciting finding that highlights the utility of these three-dimensional primary culture systems. This review has three goals: (a) to critically discuss the roles of key Cu transport enzymes in dietary Cu uptake; (b) to assess the use, utility, and limitations of organoid technology in research into nutritional Cu transport and Cu-based diseases; and (c) to highlight emerging connections between nutritional Cu homeostasis and fat metabolism.