The interaction between polymers and biological membranes has recently gained significant interest in several research areas. On the biomedical side, dendrimers, linear polyelectrolytes, and neutral copolymers find application as drug and gene delivery agents, as biocidal agents, and as platforms for biological sensors. On the environmental side, plastic debris is often disposed of in the oceans and gets degraded into small particles; therefore concern is raising about the interaction of small plastic particles with living organisms. From both perspectives, it is crucial to understand the processes driving the interaction between polymers and cell membranes. In recent times progress in computer technology and simulation methods has allowed computational predictions on the molecular mechanism of interaction between polymeric materials and lipid membranes. Here we review the computational studies on the interaction between lipid membranes and different classes of polymers: dendrimers, linear charged polymers, polyethylene glycol (PEG) and its derivatives, polystyrene, and some generic models of polymer chains. We conclude by discussing some of the technical challenges in this area and future developments.