  We give an overview of five rationalization theories for spaces
(Bousfield-Kan's $\mathbb Q$-completion; Sullivan's rationalization;
Bousfield's homology rationalization; Casacuberta-Peschke's
$\Omega$-rationalization; G\'{o}mez-Tato-Halperin-Tanr\'{e}'s $\pi_1$-fiberwise
rationalization) that extend the classical rationalization of simply connected
spaces. We also give an overview of the corresponding rationalization theories
for groups ($\mathbb Q$-completion; $H\mathbb Q$-localization; Baumslag
rationalization) that extend the classical Malcev completion.
