  Field theories on canonical noncommutative spacetimes, which are being
studied also in connection with string theory, and on $\kappa$-Minkowski
spacetime, which is a popular example of Lie-algebra noncommutative spacetime,
can be naturally constructed by introducing a suitable generating functional
for Green functions in energy-momentum space. Direct reference to a star
product is not necessary. It is sufficient to make use of the simple properties
that the Fourier transform preserves in these spacetimes and establish the
rules for products of wave exponentials that are dictated by the
non-commutativity of the coordinates. The approach also provides an elementary
description of "planar" and "non-planar" Feynman diagrams. We also comment on
the rich phenomenology emerging from the analysis of these theories.
