Nanomaterials are finding applications in most industrial sectors, from medicine to electronics. Understanding how they interact with living organisms is a fundamental step towards the production of safe-by-design nanomaterials, which is nowadays deemed necessary to guarantee economic viability. Biological membranes are the first barrier for any exogenous materials, hence understanding nanoparticle (NP)–membrane interaction is paramount for predictions of NP permeation into cells and cell damage. Surface properties are among the most important features determining NP fate in biological environments. In the present review, we first discuss experiments probing the effect of various surface properties, such as electrostatic charge, the chemical nature of ligands, and ligand patterns, on the interaction of NPs with lipid membranes. Then we describe how molecular simulations have contributed so far to a molecular-level interpretation of such experiments, and highlight the main open questions regarding the effect of surface properties on protein corona formation, NP internalization into cells, and cell damage. We conclude by summarizing the main challenges and presenting future perspectives.