Extreme high-frequency-peaked BL Lac objects (EHBLs) are the most energetic persistent sources in the universe. This contribution reports on long-term observing campaigns of tens of EHBLs that have been organized by the MAGIC collaboration to enlarge their population at VHE and understand the origin of their extreme properties. EHBLs are characterized by a spectral energy distribution (SED) featuring a synchrotron peak energy above 1 keV. Several EHBLs display a hard spectral index at very high energies (VHE; E > 100 GeV), suggesting a gamma-ray SED component peaking significantly above 1 TeV. Such extreme properties are challenging current standard emission and acceleration mechanisms. Recent studies have also unveiled intriguing disparities in the temporal characteristics of EHBLs. Some sources seem to display a persistent EHBL behaviour, while others belong to the EHBL family only temporarily. Here, we present recent results of the first hard-TeV EHBL catalog. The MAGIC observations are accompanied by an extensive multiwavelength coverage to obtain an optimal determination of the SED. This allow us to investigate leptonic and hadronic scenarios for the emission. We also present the recent detection of the EHBL RX J0812.0+0237 in the VHE band by MAGIC. Finally, we discuss a broad multiwavelength campaign on the BL Lac type object 1ES 2344+514, which showed intermittent EHBL characteristics in August 2016.
