The measurement of an astrophysical flux of high-energy neutrinos by IceCube is an importantstep towards finding the long-sought sources of cosmic rays. Nevertheless, the long exposureneutrino sky map shows no significant indication of point sources so far. The real-time follow-up of neutrino events turned out to be the most successful approach in neutrino point-sourcesearches. It brought, among others, the most compelling evidence for a neutrino point source:the flaring gamma-ray blazar TXS 0506+056 in coincidence with a single high-energy neutrinofrom IceCube (IceCube-170922A). The fast multiwavelength(MWL) follow-up of this alert waskey for establishing this coincidence and constraining the subsequent theoretical modeling for thisevent. In the long run, accurate and contemporaneous MWL spectral measurements are essentialingredients in investigating the physical processes leading to particle acceleration and emission of radiation. A deeper understanding of those processes allows us to put constraints on the potentialneutrinoemission. Herewepresentthelightcurvesandsimultaneousspectralenergydistributionsfrom November 2017 till February 2021 of MAGIC and MWL monitoring of TXS 0506+056.The more than two-year-long rise and high state of the radio light curve of TXS0506+056, whichstarted near the time of the IceCube neutrino detection, seems to have ended, as indicated bya steep decrease in the first half of 2021. We also present the theoretical interpretation of ourobservations
