The use of metal and metal oxide nanoparticles is frequently regarded as a potential solution to the issue of bacterial antibiotic resistance. Among the proposed range of nanoparticles with antibacterial properties, copper oxide nanoparticles are of particular interest. Although the antibacterial properties of copper have been known for a considerable period of time, studies on the effects of copper oxide nanomaterials with respect to biological systems have attracted considerable attention in recent years. This review presents a summary of the antibacterial properties of copper oxide nanoparticles, the mechanisms by which the antibacterial effect is realized, and the key reported methods of modifying these nanoparticles to improve their antibacterial activity. A comparative analysis of the effectiveness of these nanoparticles is presented depending on the type of microorganism, the shape of the nanoparticles, and the Gram classification of bacteria based on data from published sources. In addition, the review addresses the biological activities of copper oxide nanoparticles, including their antifungal and cytotoxic properties, as well as their “antioxidant” activity. According to the conducted analysis of the literature data, it can be concluded that copper oxide nanoparticles have a significant bacteriostatic potential with respect to a wide range of microorganisms and, in some cases, contribute to the inhibition of fungal growth. At the same time, the sensitivity of Gram-positive bacteria to the effect of copper oxide nanoparticles was often higher than that of Gram-negative bacteria.