This review summarises high resolution studies on the interface of lamellar lipid bilayers composed of the most typical lipid molecules which constitute the lipid matrix of biomembranes. The presented results were obtained predominantly by computer modelling methods. Whenever possible, the results were compared with experimental results obtained for similar systems. The first and main section of the review is concerned with the bilayer-water interface and is divided into four subsections. The first describes the simplest case, where the interface consists only of lipid head groups and water molecules and focuses on interactions between the lipid heads and water molecules; the second describes the interface containing also mono- and divalent ions and concentrates on lipid-ion interactions; the third describes direct inter-lipid interactions. These three subsections are followed by a discussion on the network of direct and indirect inter-lipid interactions at the bilayer interface. The second section summarises recent computer simulation studies on the interactions of antibacterial membrane active compounds with various models of the bacterial outer membrane. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.