Nanoscience and nanotechnology are undergoing rapid expansion owing to the promise of breakthroughs in key sectors, such as energy and medicine. As for medicine, interaction of nanomaterials with biological membranes is a key issue, both for the development of drug and gene delivery vectors and for understanding the molecular basis of nanoparticle (NP) biological activity. NP-membrane interactions are often studied with the aid of molecular simulations of model membranes, allowing to overcome the limitations in temporal and spatial resolution generally encountered by experimental techniques applied to fluid membranes. In the present review we summarize the current literature on simulations of NP-membrane interactions, focusing on small polymeric and ligand-coated NPs. Open questions emerging from experiments concern the effect of NP size, surface charge, and ligand arrangement on NP partitioning into and permeation across membranes. While simulations are contributing to significant progress in this area, some challenges remain, namely regarding the representation of the complexity of biological environments and the cooperative behavior of NPs (e.g. aggregation), as well as methodological challenges to tackle the intrinsically multi-scale nature of nano-bio interactions.