Our aim in this paper is to introduce the so-called ideal approximation theory into higher homological algebra. To this end, we introduce some important notions from approximation theory into the theory of n n -exact categories and prove some results. In particular, the higher version of notions such as ideal cotorsion pairs, phantom ideals, Salce’s Lemma and Wakamatsu’s Lemma for ideals are introduced and studied. Our results motivate the definitions and show that n n -exact categories are the appropriate context for the study of higher ideal approximation theory.