  Among the possible extensions of General Relativity that have been put
forward in order to address some long standing issues in our understanding of
the Universe, Scalar-Tensor Theories have received a lot of attention for their
simplicity. Interestingly, some of these predict a potentially observable
non-linear phenomenon, known as \textit{spontaneous scalarisation}, in the
presence of highly compact matter distributions, like the case of neutron
stars. Neutron stars are ideal laboratories to investigate the properties of
matter under extreme conditions, and in particular they are known to harbour
the strongest magnetic fields in the Universe. Here, for the first time, we
present a detailed study of magnetised neutron stars in Scalar-Tensor Theories.
First, we show that the formalism developed for the study of magnetised neutron
stars in General Relativity, based on the \textit{eXtended Conformally Flat
Condition}, can easily be extended in the presence of a non-minimally coupled
scalar field, retaining many of its numerical advantages. We then carry out a
study of the parameter space considering the two extreme geometries of purely
toroidal and purely poloidal magnetic fields, varying both the strength of the
magnetic field and the intensity of scalarisation. We compare our results with
magnetised general-relativistic solutions and un-magnetised scalarised
solutions, showing how the mutual interplay between magnetic and scalar fields
affect the magnetic and the scalarisation properties of neutron stars. In
particular, we focus our discussion on magnetic deformability, maximum mass and
range of scalarisation.
