The use of idealized scientific theories in explanations of empirical facts and regularities is problematic in two ways: they don’t satisfy the condition that the explanans is true, and they may fail to entail the explanandum. An attempt to deal with the latter problem was proposed by Hempel and Popper with their notion of approximate explanation. A more systematic perspective on idealized explanations was developed with the method of idealization and concretization by the Poznan school (Nowak, Krajewski) in the 1970s. If idealizational laws are treated as counterfactual conditionals, they can be true or truthlike, and the concretizations of such laws may increase their degree of truthlikeness. By replacing Hempel’s truth requirement with the condition that an explanatory theory is truthlike one can distinguish several important types of approximate, corrective, and contrastive explanations by idealized theories. The conclusions have important consequences for the debates about scientific realism and anti-realism.