  Black holes play a crucial role in the understanding of the gravitational
interaction. Through the direct observation of the shadow of a black hole by
the event horizon telescope and the detection of gravitational waves of merging
black holes we now start to have direct access to their properties and
behaviour, which means the properties and behaviour of gravity. This further
raised the demand for models to compare with those observations. In this
respect, an important question regarding black holes properties is to know if
they can support "hairs". While this is famously forbidden in general
relativity, in particular for scalar fields, by the so-called no-hair theorems,
hairy black holes have been shown to exist in several class of scalar-tensor
theories of gravity. In this article we investigate the existence of scalarized
black holes in scalar-torsion theories of gravity. On one hand, we find exact
solutions for certain choices of couplings between a scalar field and the
torsion tensor of a teleparallel connection and certain scalar field
potentials, and thus proof the existence of scalarized black holes in these
theories. On the other hand, we show that it is possible to establish
no-scalar-hair theorems similar to what is known in general relativity for
other choices of these functions.
