Eukaryogenesis represented a major evolutionary transition that led to the emergence of complex cells from simpler ancestors. For several decades, the most accepted scenario involved the evolution of an independent lineage of proto-eukaryotes endowed with an endomembrane system, including a nuclear compartment, a developed cytoskeleton and phagocytosis, which engulfed the alphaproteobacterial ancestor of mitochondria. However, the recent discovery by metagenomic and cultural approaches of Asgard archaea, which harbour many genes in common with eukaryotes and are their closest relatives in phylogenomic trees, rather supports scenarios based on the symbiosis of one Asgard-like archaeon and one or more bacteria at the origin of the eukaryotic cell. Here, we review the recent discoveries that led to this conceptual shift, briefly evoking current models of eukaryogenesis and the challenges ahead to discriminate between them and to establish a detailed, plausible scenario that accounts for the evolution of eukaryotic traits from those of their prokaryotic ancestors.