Lipid bilayer membranes are often represented as a continuous nonpolar slab with a certain thickness bounded by two more polar interfaces. Phenomena such as peptide binding to the membrane surface, folding, insertion, translocation, and diffusion are typically interpreted on the basis of this view. In this Perspective, I argue that this membrane representation as a hydrophobic continuum solvent is not adequate to understand peptide-lipid interactions. Lipids are not small compared to membrane-active peptides: their sizes are similar. Therefore, peptide diffusion needs to be understood in terms of free volume, not classical continuum mechanics; peptide solubility or partitioning in membranes cannot be interpreted in terms of hydrophobic mismatch between membrane thickness and peptide length; peptide folding and translocation, often involving cationic peptides, can only be understood if realizing that lipids adapt to the presence of peptides and the membrane may undergo considerable lipid redistribution in the process. In all of those instances, the detailed molecular interactions between the peptide residues and the lipid components are essential to understand the mechanisms involved.