Inteins are self-splicing polypeptides with an ability to excise themselves from flanking host protein regions with remarkable precision; in the process, they ligate flanked host protein fragments. Inteins are distributed sporadically across all three domains of life (bacteria, archaea, and unicellular eukaryotes). However, their apparent localized distribution in DNA replication, repair, and recombination proteins (the 3Rs), particularly in bacteria and archaea, is enigmatic. Our understanding of the localized distribution of inteins in the 3Rs, and their possible regulatory role in such distribution, is still only partial. Nevertheless, understanding the chemistry of post-translational self-splicing of inteins has opened up opportunities for protein chemists to modify, manipulate, and bioengineer proteins. Protein-splicing technology is adapted to a wide range of applications, starting with untagged protein purification, site-specific protein labeling, protein biotinylation, isotope incorporation, peptide cyclization, as an antimicrobial target, and so on. This review is focused on the chemistry of splicing; the localized distribution of inteins, particularly in the 3Rs and their possible role in regulating host protein function; and finally, the use of protein-splicing technology in various protein engineering applications.