Recently, the presence of fullerenes in the interstellar medium (ISM) has been confirmed and new findings suggest that these fullerenes may possibly form from polycyclic aromatic hydrocarbons (PAHs) in the ISM. Moreover, the first confirmed identification of two strong diffuse interstellar bands (DIBs) with the fullerene, C60+, connects the long standing suggestion that various fullerenes could be DIB carriers. These new discoveries justify reassessing the overall importance of interstellar fullerene compounds, including fullerenes of various sizes with endohedral or exohedral inclusions and heterofullerenes (EEHFs). The phenomenology of fullerene compounds is complex. In addition to fullerene formation in grain shattering, fullerene formation from fully dehydrogenated PAHs in diffuse interstellar clouds could perhaps transform a significant percentage of the tail of low-mass PAH distribution into fullerenes including EEHFs. But many uncertain processes make it extremely difficult to assess their expected abundance, composition and size distribution, except for the substantial abundance measured for C60+. EEHFs share many properties with pure fullerenes, such as C60, as regards stability, formation/destruction and chemical processes, as well as many basic spectral features. Because DIBs are ubiquitous in all lines of sight in the ISM, we address several questions about the interstellar importance of various EEHFs, especially as possible carriers of diffuse interstellar bands. Specifically, we discuss basic interstellar properties and the likely contributions of fullerenes of various sizes and their charged counterparts such as C60+, and then in turn: 1) metallofullerenes; 2) heterofullerenes; 3) fulleranes; 4) fullerene-PAH compounds; 5) H2@C60. From this reassessment of the literature and from combining it with known DIB line identifications, we conclude that the general landscape of interstellar fullerene compounds is probably much richer than heretofore realized. EEHFs, together with pure fullerenes of various sizes, have many properties necessary to be suitably carriers of DIBs: carbonaceous nature; stability and resilience in the harsh conditions of the ISM; existing with various heteroatoms and ionization states; relatively easy formation; few stable isomers; spectral lines in the right spectral range; various and complex energy internal conversion; rich Jahn-Teller fine structure. This is supported by the first identification of a DIB carrier as C60+. Unfortunately, the lack of any precise information about the complex optical spectra of EEHFs and most pure fullerenes other than C60 and about their interstellar abundances still precludes definitive assessment of the importance of fullerene compounds as DIB carriers. Their compounds could significantly contribute to DIBs, but it still seems difficult that they are the only important DIB carriers. Regardless, DIBs appear as the most promising way of tracing the interstellar abundances of various fullerene compounds if the breakthrough in identifying C60+ as a DIB carrier can be extended to more spectral features through systematic studies of their laboratory gas-phase spectroscopy.