  Following the discovery of high-energy (HE; $E>10\,{\rm MeV}$) and
very-high-energy (VHE; $E>100\,{\rm GeV}$) $\gamma$-ray emission from the
low-frequency-peaked BL~Lac (LBL) object AP Librae, its electromagnetic
spectrum is studied over 60 octaves in energy. Contemporaneous data in radio,
optical and UV together with the $\gamma$-ray data are used to construct the
most precise spectral energy distribution of this source. The data have been
found to be modeled with difficulties with single zone homogeneous leptonic
synchrotron self-Compton (SSC) radiative scenarios due to the unprecedented
width of the high-energy component when compared to the lower-energy component.
The two other LBL objects also detected at VHE appear to have similar modeling
difficulties. Nevertheless, VHE $\gamma$ rays produced in the extended jet
could account for the VHE flux observed by H.E.S.S.
