Evolution of exon-intron structure of eukaryotic genes has been a matter of long-standing, intensive debate. The introns-early concept, later rebranded 'introns first' held that protein-coding genes were interrupted by numerous introns even at the earliest stages of life's evolution and that introns played a major role in the origin of proteins by facilitating recombination of sequences coding for small protein/peptide modules. The introns-late concept held that introns emerged only in eukaryotes and new introns have been accumulating continuously throughout eukaryotic evolution. Analysis of orthologous genes from completely sequenced eukaryotic genomes revealed numerous shared intron positions in orthologous genes from animals and plants and even between animals, plants and protists, suggesting that many ancestral introns have persisted since the last eukaryotic common ancestor (LECA). Reconstructions of intron gain and loss using the growing collection of genomes of diverse eukaryotes and increasingly advanced probabilistic models convincingly show that the LECA and the ancestors of each eukaryotic supergroup had intron-rich genes, with intron densities comparable to those in the most intron-rich modern genomes such as those of vertebrates. The subsequent evolution in most lineages of eukaryotes involved primarily loss of introns, with only a few episodes of substantial intron gain that might have accompanied major evolutionary innovations such as the origin of metazoa. The original invasion of self-splicing Group II introns, presumably originating from the mitochondrial endosymbiont, into the genome of the emerging eukaryote might have been a key factor of eukaryogenesis that in particular triggered the origin of endomembranes and the nucleus. Conversely, splicing errors gave rise to alternative splicing, a major contribution to the biological complexity of multicellular eukaryotes. There is no indication that any prokaryote has ever possessed a spliceosome or introns in protein-coding genes, other than relatively rare mobile self-splicing introns. Thus, the introns-first scenario is not supported by any evidence but exon-intron structure of protein-coding genes appears to have evolved concomitantly with the eukaryotic cell, and introns were a major factor of evolution throughout the history of eukaryotes.