Magnetic nanoparticles became increasingly interesting in recent years as a result of their tailorable size-dependent properties, which enable their use in a wide range of applications. One of their emerging applications is biomedicine; in particular, bimetallic nickel/copper magnetic nanoparticles (NiCu MNPs) are gaining momentum as a consequence of their unique properties that are suitable for biomedicine. These characteristics include stability in various chemical environments, proven biocompatibility with various cell types, and tunable magnetic properties that can be adjusted by changing synthesis parameters. Despite the obvious potential of NiCu MNPs for biomedical applications, the general interest in their use for this purpose is rather low. Nevertheless, the steadily increasing annual number of related papers shows that increasingly more researchers in the biomedical field are studying this interesting formulation. As with other MNPs, NiCu-based formulations were examined for their application in magnetic hyperthermia (MH) as one of their main potential uses in clinics. MH is a treatment method in which cancer tissue is selectively heated through the localization of MNPs at the target site in an alternating magnetic field (AMF). This heating destroys cancer cells only since they are less equipped to withstand temperatures above 43 °C, whereas this temperature is not critical for healthy tissue. Superparamagnetic particles (e.g., NiCu MNPs) generate heat by relaxation losses under an AMF. In addition to MH in cancer treatment, which might be their most beneficial potential use in biomedicine, the properties of NiCu MNPs can be leveraged for several other applications, such as controlled drug delivery and prolonged localization at a desired target site in the body. After a short introduction that covers the general properties of NiCu MNPs, this review explores different synthesis methods, along with their main advantages and disadvantages, potential surface modification approaches, and their potential in biomedical applications, such as MH, multimodal cancer therapy, MH implants, antibacterial activity, and dentistry.