  Motivated by the recent interest in underground experiments phenomenology, we
review the main aspects of one specific non-commutative space-time model, based
on the Groenewold-Moyal plane algebra, the $\theta$-Poincar\'e space-time. In
the $\theta$-Poincar\'e scenario, the Lorentz co-algebra is deformed
introducing a non-commutativity of space-time coordinates. In such a theory, a
new quantum field theory in non-commutative space-time can be reformulated.
Tackling on several conceptual misunderstanding and technical mistakes in the
literature, we will focus on several issues such: $i)$ the construction of
fields theories in $\theta$-Poincar\'e; $ii)$ the unitarity of the S-matrix;
$iii)$ the violation of locality, $iv)$ the violation of the spin statistic
theorem and the Pauli principle; $v)$ the observables for underground
experiments.
