All life on earth can be naturally classified into cellular life forms and virus-like selfish elements, the latter being fully dependent on the former for their reproduction. Cells are reproducers that not only replicate their genome but also reproduce the cellular organization that depends on semipermeable, energy-transforming membranes and cannot be recovered from the genome alone, under the famous dictum of Rudolf Virchow, Omnis cellula e cellula. In contrast, simple selfish elements are replicators that can complete their life cycles within the host cell starting from genomic RNA or DNA alone. The origin of the cellular organization is the central and perhaps the hardest problem of evolutionary biology. I argue that the origin of cells can be understood only in conjunction with the origin and evolution of selfish genetic elements. A scenario of precellular evolution is presented that involves cohesion of the genomes of the emerging cellular life forms from primordial pools of small genetic elements that eventually segregated into hosts and parasites. I further present a model of the coevolution of primordial membranes and membrane proteins, discuss protocellular and non-cellular models of early evolution, and examine the habitats on the primordial earth that could have been conducive to precellular evolution and the origin of cells.