Recent major discoveries in membrane biophysics hold the key to a modern understanding of the origin of life on Earth. Membrane bilayer vesicles have been shown to provide a multifaceted microenvironment in which protometabolic reactions could have developed. Cell-membrane-like aggregates of amphiphilic molecules capable of retaining encapsulated oligonucleotides have been successfully created in the laboratory. Sophisticated laboratory studies on the origin of life now show that elongation of the DNA primer takes place inside fatty acid vesicles when activated nucleotide nutrients are added to the external medium. These studies demonstrate that cell-like vesicles can be sufficiently permeable to allow for the intake of charged molecules such as activated nucleotides, which can then take part in copying templates in the protocell interior. In this Review we summarize recent experiments in this area and describe a possible scenario for the origin of primitive cells, with an emphasis on the elongation of encapsulated nucleotides.