Graphene and graphene oxide (GO) structures and their reduced forms, e.g., GO paper and partially or fully reduced three-dimensional (3D) aerogels, are at the forefront of materials design for extensive biomedical applications that allow for the proliferation and differentiation/maturation of cells, drug delivery, and anticancer therapies. Various viability tests that have been conducted in vitro on human cells and in vivo on mice reveal very promising results, which make graphene-based materials suitable for real-life applications. In this review, we will give an overview of the latest studies that utilize graphene-based structures and their composites in biological applications and show how the biomimetic behavior of these materials can be a step forward in bridging the gap between nature and synthetically designed graphene-based nanomaterials.