Nano-sized materials have great potential as drug carriers for nanomedicine applications. Thanks to their size, they can exploit the cellular machinery to enter cells and be trafficked intracellularly, thus they can be used to overcome some of the cellular barriers to drug delivery. Nano-sized drug carriers of very different properties can be prepared, and their surface can be modified by the addition of targeting moieties to recognize specific cells. However, it is still difficult to understand how the material properties affect the subsequent interactions and outcomes at cellular level. As a consequence of this, designing targeted drugs remains a major challenge in drug delivery. Within this context, we discuss the current understanding of the initial steps in the interactions of nano-sized materials with cells in relation to nanomedicine applications. In particular, we focus on the difficult interplay between the initial adhesion of nano-sized materials to the cell surface, the potential recognition by cell receptors, and the subsequent mechanisms cells use to internalize them. The factors affecting these initial events are discussed. Then, we briefly describe the different pathways of endocytosis in cells and illustrate with some examples the challenges in understanding how nanomaterial properties, such as size, charge, and shape, affect the mechanisms cells use for their internalization. Technical difficulties in characterizing these mechanisms are presented. A better understanding of the first interactions of nano-sized materials with cells will help to design nanomedicines with improved targeting.