The folding and function of membrane proteins is controlled not only by specific but also by unspecific interactions with the constituent lipids. In this review, we focus on the influence of the spontaneous lipid curvature on the folding and insertion of peptides and proteins in membranes. Amphiphilic α-helical peptides, as represented by various antimicrobial sequences, are compared with β-barrel proteins, which are found in the outer membrane of Gram-negative bacteria. It has been shown that cationic amphiphilic peptides are always surface-bound in lipids with a negative spontaneous curvature like POPC, i.e. they are oriented parallel to the membrane plane. On the other hand, in lipids like DMPC with a positive curvature, these peptides can get tilted or completely inserted in a transmembrane state. Remarkably, the folding and spontaneous membrane insertion of β-barrel outer membrane proteins also proceeds more easily in lipids with a positive intrinsic curvature, while it is hampered by negative curvature. We therefore propose that a positive spontaneous curvature of the lipids promotes the ability of a surface-bound molecule to insert more deeply into the bilayer core, irrespective of the conformation, size, or shape of the peptide, protein, or folding intermediate. This article is part of a Special Issue entitled: Lipid-protein interactions.