  While active galactic nuclei with relativistic jets have long been prime
candidates for the origin of extragalactic cosmic rays and neutrinos, the BL
Lac object TXS 0506+056 is the first astrophysical source observed to be
associated with some confidence ($\sim 3\sigma$) with a high-energy neutrino,
IceCube-170922A, detected by the IceCube Observatory. The source was found to
be active in high-energy gamma-rays with Fermi-LAT and in very-high-energy
gamma-rays with the MAGIC telescopes. To consistently explain the observed
neutrino and multi-wavelength electromagnetic emission of TXS 0506+056, we
investigate in detail single-zone models of lepto-hadronic emission, assuming
co-spatial acceleration of electrons and protons in the jet, and synchrotron
photons from the electrons as targets for photo-hadronic neutrino production.
The parameter space concerning the physical conditions of the emission region
and particle populations is extensively explored for scenarios where the
gamma-rays are dominated by either 1) proton synchrotron emission or 2)
synchrotron-self-Compton emission, with a subdominant but non-negligible
contribution from photo-hadronic cascades in both cases. We find that the
latter can be compatible with the neutrino observations, while the former is
strongly disfavoured due to the insufficient neutrino production rate.
