Metal–organic frameworks (MOFs) have emerged as a versatile class of porous crystalline materials due to their tunable structures, large surface areas, and diverse functionalities. Among them, copper-based MOFs (Cu-MOFs) are of particular interest because of the redox activity of copper centers, flexible coordination chemistry, and high affinity for various organic linkers. These features make Cu-MOFs promising candidates for a wide range of applications spanning catalysis, energy conversion and storage, and chemical sensing. This review highlights recent advances in the synthesis and design strategies of Cu-MOFs, including conventional solvothermal and hydrothermal routes, microwave- and sonochemical-assisted methods, electrochemical synthesis, and postsynthetic modifications. Particular emphasis is placed on the ability of these synthetic approaches to tune particle size, morphology, porosity, and stability, which, in turn, dictate their functional performance. The catalytic applications of Cu-MOFs are critically examined, with a focus on photocatalysis, electrocatalysis, and heterogeneous catalytic processes for pollutant degradation, hydrogen production, and carbon dioxide reduction. In the context of energy storage, the integration of Cu-MOFs into supercapacitors and batteries is discussed, highlighting their roles in enhancing the capacity, conductivity, and cycling stability. Furthermore, the potential of Cu-MOFs as sensitive and selective sensing platforms for gases, biomolecules, and environmental pollutants is explored, underscoring their versatility beyond catalytic applications. Despite rapid progress, key challenges remain in scaling up the synthesis, ensuring long-term structural stability, and integrating Cu-MOFs into practical devices. Future research directions include the development of cost-effective green synthesis methods, hybrid composite materials with enhanced conductivity, and defect and interface engineering to tailor activity and durability. Overall, Cu-MOFs represent a highly adaptable platform whose continued advancement may significantly impact sustainable energy technologies, environmental remediation, and next-generation sensing systems.