The Martian Global Climate Model (GCM) of the Laboratoire de Météorologie Dynamique (LMD) is developped in collaboration with several European teams (LATMOS, IAA Granada, University of Oxford, The Open University), with support from ESA and CNES. Using physically-based schemes, this model strives to reproduce the detailed behavior of the Martian climate, mainly related to the CO2, the water, and the dust cycles, and includes photochemistry. Using comparisons of GCM simulations with available observations allow to interpret the later and sometimes reveal which processes remain poorly modeled. The ongoing implementation of the latest improvements developped by our team has already provided insights on some discrepancies, and have lead to the generation of a new version of our GCM ; in particular : - The water cycle has been improved by introducing a representation of sub-grid scale clouds (when only a fraction of the mesh is covered by clouds), and by increasing the vertical resolution, which better represents the intense convection in some night-time clouds (Spiga et al. 2017). - The implementation of a parametrization of non-orographic gravity waves, which seem to be crucial components of the atmospheric circulation, significantly improves the simulated thermal structure. - A parameterization of « rocket dust storms » (Spiga et al. 2013) now alllows to generate the enigmatic detached dust layers observed between 20 and 30 km altitude, but only during the dust storm season (Wang et al. 2018). In order to also obtain them during the clear season, a parametrization of dust injection by winds at the top of mountains has been initiated. - Microphysics of CO2 clouds, with the possibility to nucleate CO2 on water ice nuclei, has also been implemented and is currently being validated. - We are moreover also working on the implementation of a new atmospheric chemistry solver (Cariolle et al. 2017), and the improvement of the representation of the low (near-surface) ionosphere (Cardnell et al. 2016).