  We have investigated some issues relevant for the possibility to construct
physical theories on the $\kappa$-Minkowski noncommutative spacetime. The
notion of field in $\kappa$-Minkowski has been introduced by generalizing the
Weyl system/map formalism and a comparative study of the star products arising
from this generalization has been done. A line of analysis of the symmetries of
$\kappa$-Minkowski has been proposed that relies on the possibility to find a
"maximally"-symmetric action which is invariant under a 10-generator
Poincar\'e-like symmetry algebra. The equation of motion for scalar particles
has been obtained by a generalized variational principle. An extension of the
Dirac equation for spin-1/2 particles has been proposed by using a
five-dimensional differential calculus on $\kappa$-Minkowski.
