A key function of biological membranes is to provide mechanisms for the controlled transport of ions, nutrients, metabolites, peptides and proteins between a cell and its environment. We are using computer simulations to study several processes involved in transport. In model membranes, the distribution of small molecules can be accurately calculated; we are making progress towards understanding the factors that determine the partitioning behaviour in the inhomogeneous lipid environment, with implications for drug distribution, membrane protein folding and the energetics of voltage gating. Lipid bilayers can be simulated at a scale that is sufficiently large to study significant defects, such as those caused by electroporation. Computer simulations of complex membrane proteins, such as potassium channels and ATP-binding cassette (ABC) transporters, can give detailed information about the atomistic dynamics that form the basis of ion transport, selectivity, conformational change and the molecular mechanism of ATP-driven transport. This is illustrated in the present review with recent simulation studies of the voltage-gated potassium channel KvAP and the ABC transporter BtuCD.