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 H_0_. Type II Cepheids are also important distance indicator and tracers of old stellar populations. The recent Data Release 2 (DR2) of the Gaia Spacecraft includes photometry and parallaxes for thousands of classical and type II cepheids. We aim at reviewing the classification of Gaia DR2 Cepheids and to derive precise PL/PW for Magellanic Cloud (MCs) and Galactic Cepheids. Information from the literature and the 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 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 Gaia} bands, finding non-conclusive results. According to our analysis, the zero point of the Gaia DR2 parallaxes as estimated from Classical and Type II Cepheids seems to be likely underestimated by ~0.07mas, in full agreement with recent literature. The next Gaia data releases are expected to fix this zero point offset to eventually allow a determination of H_0_ to less than 1%.