Fusion of lipid-enveloped viruses with the cellular plasma membrane or the endosome membrane is mediated by viral envelope proteins that undergo large conformational changes following binding to receptors. The HIV-1 fusion protein gp41 undergoes a transition into a "six-helix bundle" after binding of the surface protein gp120 to the CD4 receptor and a co-receptor. Synthetic peptides that mimic part of this structure interfere with the formation of the helix structure and inhibit membrane fusion. This approach also works with the S spike protein of SARS-CoV-2. Here we review the peptide inhibitors of membrane fusion involved in infection by influenza virus, HIV-1, MERS and SARS coronaviruses, hepatitis viruses, paramyxoviruses, flaviviruses, herpesviruses and filoviruses. We also describe recent computational methods used for the identification of peptide sequences that can interact strongly with protein interfaces, with special emphasis on SARS-CoV-2, using the PePI-Covid19 database.