  A fraction of the active supermassive black holes at the centers of galaxies
in our Universe are capable of launching extreme kiloparsec-long relativistic
jets. These jets are known multiband (radio to $\gamma$-ray) and multimessenger
(neutrino) emitters, and some of them have been monitored over several decades
at all accessible wavelengths. However, many open questions remain unanswered
about the processes powering these highly energetic phenomena. These jets
intrinsically produce soft-to-hard X-ray emission that extends from
$E\sim0.1\,\rm keV$ up to $E>100\,\rm keV$. Simultaneous broadband X-ray
coverage, combined with excellent timing and imaging capabilities, is required
to uncover the physics of jets. Indeed, truly simultaneous soft-to-hard X-ray
coverage, in synergy with current and upcoming high-energy facilities (such as
IXPE, COSI, CTAO, etc.) and neutrino detectors (e.g., IceCube), would enable us
to disentangle the particle population responsible for the high-energy
radiation from these jets. A sensitive hard X-ray survey ($F_{8-24\,\rm
keV}<10^{-15}\,\rm erg~cm^{-2}~s^{-1}$) could unveil the bulk of their
population in the early Universe. Acceleration and radiative processes
responsible for the majority of their X-ray emission would be pinned down by
microsecond timing capabilities at both soft and hard X-rays. Furthermore,
imaging jet structures for the first time in the hard X-ray regime could
unravel the origin of their high-energy emission. The proposed Probe-class
mission concept High Energy X-ray Probe (HEX-P) combines all these required
capabilities, making it the crucial next-generation X-ray telescope in the
multi-messenger, time-domain era. HEX-P will be the ideal mission to unravel
the science behind the most powerful accelerators in the universe.
