The physics of blazar jets in the context of multi-wavelength and multi-messenger astronomy

Blazars, active galactic nuclei with relativistic jets pointed to the observer, emit radiation across the spectrum and can produce neutrinos via hadronic processes. Being neutral and nearly massless, neutrinos offer unique insights into energetic astrophysical processes. The flaring gamma-ray blazar TXS0506+056 detected in spatial coincidence with the IceCube-170922A neutrino event confirmed theoretical expectations, emphasising the need for further observational insights into the neutrino-blazar connection. A part of this thesis investigates high-resolution VLBI (parsec-scale) regions of gamma-ray blazars coinciding with IceCube Neutrino Observatory detections. Our VLBI follow-ups aim to identify neutrino-emitting blazars by examining radio properties like coincident flares and jet morphology features. While some of the examined sources show hints of elevated activity at the neutrino arrival, further VLBI and MWL observations are essential for understanding the neutrino production mechanisms in blazars. The low-energy part of blazar broadband SEDs is explained with synchrotron radiation. Regarding the high-energy part, the ongoing debate involves hypotheses on hadronic processes and Inverse Compton scatterings - sometimes with the same low-energy synchrotron photons (SSC models). VHE (E > 100 GeV) long-term monitoring, as with the MAGIC telescopes, complemented with MWL observations, contributes to the comprehensive investigations of blazar emission mechanisms. A part of this thesis analyses a three-year (2020-2022) MWL monitoring of the blazar 1ES1959+650 during a low state. The flux and spectral variability are studied and the SEDs during different low and high VHE states in these three years are interpreted with SSC models. Findings are compared with past active and non-active states. The two parts of this project aim to deepen our understanding of particle acceleration complementarily, using radio and gamma-ray (+MWL) observations, considering future crucial advancements with the SKA and the CTA observatories.