In recent years, progresses in nanotechnology have established the foundations for implementing nanomachines capable of carrying out simple but significant tasks. Under this stimulus, researchers have been proposing various solutions for realizing nanoscale communications, considering both electromagnetic and biological communications. Their aim is to extend the capabilities of nanodevices, so as to enable the execution of more complex tasks by means of mutual coordination, achievable through communications. However, although most of these proposals show how devices can communicate at the nanoscales, they leave in the background specific applications of these new technologies. Thus, this paper shows an overview of the actual and potential applications that can rely on a specific class of such communications techniques, commonly referred to as molecular communications. In particular, we focus on health-related applications. This decision is due to the rapidly increasing interests of research communities and companies to minimally invasive, biocompatible, and targeted health-care solutions. Molecular communication techniques have actually the potentials of becoming the main technology for implementing advanced medical solution. Hence, in this paper we provide a taxonomy of potential applications, illustrate them in some detail, along with the existing open challenges for them to be actually deployed, and draw future perspectives.