  Classical Cepheids are the most important primary indicators for the
extragalactic distance scale. Establishing the precise zero points of their
Period-Luminosity and Period-Wesenheit (PL/PW) relations has profound
consequences on the estimate of $\rm H_0$. Type II Cepheids are also important
distance indicator and tracers of old stellar populations. The recent Data
Release 2 (DR2) of the {\it Gaia} Spacecraft includes photometry and parallaxes
for thousands of classical and type II cepheids. We aim at reviewing the
classification of {\it Gaia} DR2 Cepheids and to derive precise PL/PW for
Magellanic Cloud (MCs) and Galactic Cepheids. Information from the literature
and the {\it Gaia} astrometry and photometry are adopted to assign DR2 Galactic
Cepheids to the classes: Classical, Anomalous and Type II Cepheids. We
re-classify the DR2 Galactic Cepheids and derive new precise PL/PW relations in
the {\it Gaia} passbands for the MCs and Milky Way Cepheids. We investigated
for the first time the dependence on metallicity of the $PW$ relation for
Classical Cepheids in the {\it Gaia} bands, finding non-conclusive results.
According to our analysis, the zero point of the {\it Gaia} DR2 parallaxes as
estimated from Classical and Type II Cepheids seems to be likely underestimated
by $\sim$0.07 mas, in full agreement with recent literature. The next {\it
Gaia} data releases are expected to fix this zero point offset to eventually
allow a determination of $\rm H_0$ to less than 1\%.
