Copper current collectors (Cu CCs) impact the production technology and performance of many electrochemical devices by their unique properties and reliable operation. The efficiency of the related processes and the operation of the electrochemical devices could be significantly improved by optimization of the Cu CCs. Metallic Cu plays an important role in electrochemical energy storage and electrocatalysis, primarily as a conducting substrate on which the chemical processes take place. Li nucleation and growth can be influenced by the current collector by modulating the local current density and Li ion transport. For example, the commonly used planar Cu CC does not perform satisfactorily; therefore, a high number of different modifications of Cu CCs have been proposed and reported in the literature for minimizing the local current density, hindering Li dendrite formation, and improving the Coulombic efficiency. Here, we provide an updated critical overview of the basic strategies of 3D Cu CC structuring, methodologies for analyzing these structures, and approaches for effective control over their most relevant properties. These methods are described in the context of their practical usefulness and applicability in an effort to aid in their easy implementation by research groups and private companies with established traditions in electrochemistry and plating technology. Furthermore, the current overview could be helpful for specialists with experience in associated fields of knowledge such as materials engineering and surface finishing, where electrochemical methods are frequently applied. Motivated by the importance of the final application of Cu CCs in energy storage devices, this review additionally discusses the relationship between CC properties and the functional parameters of the already-implemented electrodes.