Among various metal chalcogenides, metal oxides and phases of copper sulfide, copper(II) sulfide (covellite, CuS) nanostructures have enjoyed special attentiveness from researchers and scientists across the world owing to their complicated structure, peculiar composition and valency, attractive and panoramic morphologies, optical and electrical conductivity, less toxicity, and biocompatibility that can be exploited in advanced and technological applications. This review paper presents a brief idea about crystal structure, composition, and various chemical methods. The mechanism and effect of reaction parameters on the evolution of versatile and attractive morphologies have been described. Physical properties of CuS and its hybrid nanostructures, such as morphology and optical, mechanical, electrical, thermal, and thermoelectrical properties, have been carefully reviewed. A concise account of CuS and its hybrid nanostructures’ diverse applications in emerging and recent applications such as energy storage devices (lithium-ion batteries, supercapacitance), sensors, field emission, photovoltaic cells, organic pollutant removal, electromagnetic wave absorption, and emerging biomedical field (drug delivery, photothermal ablation, deoxyribonucleic acid detection, anti-microbial and theranostic) has also been elucidated. Finally, the prospects, scope, and challenges of CuS nanostructures have been discussed precisely.