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Extreme high-energy peaked BL Lac objects (EHBLs) are an emerging class ofblazars with exceptional spectral properties. In blazars, the spectral energydistribution (SED) is dominated by the non-thermal emission of the relativisticjet, and consists of two main broad humps. For the EHBLs, these two componentspeak in the X-ray and GeV-TeV bands, respectively. Although the number of TeVdetected extreme blazars is very limited, recent observations by ImagingAtmospheric Cherenkov Telescopes (IACTs) have revealed that in some of them theenergy of the second peak exceeds several TeV (e.g. 1ES 0229+200). Theirexceptional hard TeV spectra represent a challenge for the standard leptonicmodeling, and a possible hadronic contribution may make these objectshigh-energy neutrinos producers. Moreover, they are important for theimplications on the indirect measurements of the extragalactic background lightand of the intergalactic magnetic field. In this contribution, we perform acomparative study of the multi-wavelength spectral energy distributions of asample of hard X-ray selected EHBL objects. The analysis suggests that the EHBLclass is not homogeneous, and a possible sub-classification may be unveiledwith TeV gamma-ray observations of the candidates. With the purpose ofincreasing their number and settle their statistics, we discuss the potentialdetectability of the currently undetected TeV-emitting EHBLs in our sample bycurrent and next generation of IACTs.

Extreme high-energy peaked BL Lac objects and their TeV gamma-ray emission: are they a homogeneous population?