Graphene, a unique two-dimensional single-atom-thin nanomaterial with exceptional structural, mechanical, and electronic properties, has spurred an enormous interest in many fields, including biomedical applications, which at the same time ignites a growing concern on its biosafety and potential cytotoxicity to human and animal cells. In this review, we present a summary of some very recent studies on this important subject with both experimental and theoretical approaches. The molecular interactions of graphene with proteins, DNAs, and cell membranes (both bacteria and mammalian cells) are discussed in detail. Severe distortions in structures and functions of these biomacromolecules by graphene are identified and characterized. For example, the graphene is shown to disrupt bacteria cell membranes by insertion/cutting as well as destructive extraction of lipid molecules directly. More interestingly, this cytotoxicity has been shown to have implications in de novo design of nanomedicine, such as graphene-based band-aid, a potential 'green' antibiotics due to its strong physical-based (instead of chemical-based) antibacterial capability. These studies have provided a better understanding of graphene nanotoxicity at both cellular and molecular levels, and also suggested therapeutic potential by using graphene's cytotoxicity against bacteria cells. For further resources related to this article, please visit the WIREs website. Conflict of interest: The authors have declared no conflicts of interest for this article.