Correlation among morphological, structural and hardness characteristics of electrodeposited copper coatings is presented in this review paper. Cu coatings were produced applying constant galvanostatic (DC) and pulsating current (PC) regimes on hard silicon (Si(111)) and brass substrates. The parameters of the electrochemical deposition were analyzed, which include the kinds of electrolyte and cathode, the coating thickness and the electrolyte stirring, as well as the parameters defining PC regime, such as the average current density and the current density amplitude, were analyzed. Morphology and structure of Cu coatings were examined by scanning electron microscope (SEM), atomic force microscope (AFM) and by X-ray diffraction (XRD), while hardness was examined by Vickers microindentation. The coatings of Cu on both Si(111) and brass cathodes belong to “soft film (coating) on hard substrate” composite hardness system, and the Chicot–Lesage (C–L) composite hardness model was applied to estimate a hardness of the Cu coatings. Analyzing the examined parameters and regimes of electrodeposition, the critical relative indentation depth (RID)c of 0.14 has been defined by the C–L model. Based on done analyses, it is shown that this RID value, separating a zone where measured hardness corresponds to the coating hardness and a zone where it is necessary to apply the C–L model to determine an absolute hardness of the Cu coatings, has an universal character for the electrolytically produced Cu coatings on Si(111) and brass substrates.