  The gamma-ray blazar TXS 0506+056, was discovered in VHE gamma-rays by the
MAGIC telescopes in 2017 in a follow-up campaign of a high energy neutrino
event IceCube-170922A (IC+Fermi+MAGIC++, Science 361, eaat1378 (2018)).
Subsequent multivawelenght (MWL) observations and theoretical modeling in a
frame of hadro-leptonic emission confirmed that this source could be a
potential cosmic ray and neutrino emitter (MAGIC Collaboration, Ansoldi et al.,
(2018)). This is, by far, the most significant association between a
high-energy neutrino and an astrophysical source emitting gamma rays and
X-rays. TXS 0506+056 is a key object to help the astrophysics community to
establish connections between high-energy neutrinos and astrophysical sources.
Accurate and contemporaneous MWL spectral measurements are essential
ingredients to achieve this goal. In the conference, we present the
measurements from the MAGIC and MWL monitoring of this source, spanning the
time period from November 2017 till February 2019. These include the lowest VHE
gamma-ray emission state measured from this source so far as well as a flaring
episode in December 2018.
