Recently, the presence of fullerenes in the interstellar medium (ISM) has been confirmed especially with the first confirmed identification of two strong diffuse interstellar bands (DIBs) with C60+. This justifies reassesing the importance of interstellar fullerenes of various sizes with endohedral or exohedral inclusions and heterofullerenes (EEHFs). The phenomenology of fullerenes is complex. In addition to fullerene formation in shock shattering, fully dehydrogenated PAHs in diffuse interstellar (IS) clouds could perhaps efficiently transform into fullerenes including EEHFs. But it is extremely difficult to assess their expected abundance, composition and size distribution, except for C60+. EEHFs share many properties with C60, as regards stability, formation/destruction and chemical processes, and many basic spectral features. We address the interstellar importance of various EEHFs as possible DIB carriers. Specifically, we discuss IS properties and the contributions of fullerenes of various sizes and charge such as C60+, metallofullerenes, heterofullerenes, fulleranes, fullerene-PAH compounds, H2@C60. We conclude that the landscape of interstellar fullerenes is probably much richer than heretofore realized. EEHFs, together with pure fullerenes of various sizes, have properties necessary to be suitably carriers of DIBs: carbonaceous nature; stability and resilience in the ISM; various heteroatoms and ionization states; relatively easy formation; few stable isomers; right spectral range; energy internal conversion; Jahn-Teller fine structure. This is supported by the C60+ DIBs. But, the lack of information about optical spectra other than C60 and IS abundances still precludes definitive assessment of the importance of fullerenes as DIB carriers. Their compounds could significantly contribute to DIBs, but it still seems difficult that they are the only important DIB carriers.
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