Extreme high-energy peaked BL Lac objects (EHBLs) are an emerging class of blazars with exceptional spectral properties. In blazars, the spectral energy distribution (SED) is dominated by the non-thermal emission of the relativistic jet, and consists of two main broad humps. For the EHBLs, these two components peak in the X-ray and GeV-TeV bands, respectively. Although the number of TeV detected extreme blazars is very limited, recent observations by Imaging Atmospheric Cherenkov Telescopes (IACTs) have revealed that in some of them the energy of the second peak exceeds several TeV (e.g. 1ES 0229+200). Their exceptional hard TeV spectra represent a challenge for the standard leptonic modeling, and a possible hadronic contribution may make these objects high-energy neutrinos producers. Moreover, they are important for the implications on the indirect measurements of the extragalactic background light and of the intergalactic magnetic field. In this contribution, we perform a comparative study of the multi-wavelength spectral energy distributions of a sample of hard X-ray selected EHBL objects. The analysis suggests that the EHBL class is not homogeneous, and a possible sub-classification may be unveiled with TeV gamma-ray observations of the candidates. With the purpose of increasing their number and settle their statistics, we discuss the potential detectability of the currently undetected TeV-emitting EHBLs in our sample by current and next generation of IACTs.
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