Following the discovery of high-energy (HE; E > 10 MeV) and very-high-energy (VHE; E > 100 GeV) γ-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 (non-simultaneous) γ-ray data are used to construct the most precise spectral energy distribution of this source. The data have been found to be modelled with difficulties with single-zone homogeneous leptonic synchrotron self-Compton (SSC) radiative scenarios due to the unprecedented width of the HE component when compared to the lower-energy component. The two other LBL objects also detected at VHE appear to have similar modelling difficulties. Nevertheless, VHE γ-rays produced in the extended jet could account for the VHE flux observed by HESS.