Binding affinities of charged molecules, such as drugs, amino acids, ions and pollutants, on cellular membranes regulate many of their biological functions. For example, signalling domains in proteins often contain charged residues and interact with membranes in an iondependent manner, 1,4-6 translocation of drugs through membranes depends on their charge state, 7 and bioaccumulation of charged pollutants can be related to their membrane affinity. Such processes are particularly poorly understood for charged molecules because their binding to membranes is significantly more difficult to study than for neutral molecules. Therefore, better understanding and predictive models for membrane binding of charged molecules would benefit applications in a wide range of fields, such as designing drugs with better translocation properties, and understanding cell signalling and bioaccumulation of potentially toxic molecules. For neutral molecules, the water-oil (often octanol) partition coefficients correlate well with the binding data on model membranes and their binding affinities can be captured equally well by theoretical models with atomistic and continuum level descriptions. However, measurements of water-oil partition coefficients are problematic for charged molecules due to the charge neutralization in both phases. Furthermore, experimental data on lipid binding affinity is more scarce, and a complex electrostatic environment at membrane interfaces, created by dipoles of lipids and water molecules, complicates theoretical analyses. Incorporation of membrane dipole potential in continuum models improves the results, 14 but atomistic resolution description is needed to fully capture the complexity of electrostatic and other interactions between lipids, water and charged molecules at membrane interfaces.