The origin of the presence of geological and mineralogical evidence that liquid water flowed on the surface of early Mars is now a 50-year-old mystery. It has been proposed (Segura et al., 2002(Segura et al., , 2008(Segura et al., , 2012 that bolide impacts could have triggered a long-term climate change, producing precipitation and runoff that may have altered the surface of Mars in a way that could explain (at least part of) this evidence. Here we use a hierarchy of numerical models (a 3-D Global Climate Model, a 1-D radiative-convective model and a 2-D Mantle Dynamics model) to test that hypothesis and more generally explore the environmental effects of very large bolide impacts (D impactor > 100 km, or D crater > 600 km) on the atmosphere, surface and interior of early Mars.Using a combination of 1-D and 3-D climate simulations, we show that the environmental effects of the largest impact events recorded on Mars are characterized by: (i) a short impact-induced warm period (several tens of Earth years for the surface and atmosphere to be back to ambient conditions after very large impact events); (ii) a low amount of hydrological cycling of water (because there is no surface re-evaporation of precipitation). The total cumulated amount of precipitation (rainfall) can be reasonably well approximated by the initial post-impact atmospheric reservoir of water vapour (coming from the impactor, the impacted terrain and from the sublimation of permanent ice reservoirs heated by the hot ejecta layer); (iii) deluge-style precipitation (∼2.6 m Global Equivalent Layer of surface precipitation per Earth year for our reference simulation, quantitatively in agreement with previous 1-D cloud free climate calculations of Segura et al. 2002), and (iv) precipitation patterns that are uncorrelated with the observed regions of valley networks.However, we show that the impact-induced stable runaway greenhouse state predicted by Segura et al. (2012) is physically inconsistent. We nevertheless confirm the results of Segura et al. (2008) and Urata and Toon (2013) that water ice clouds could in theory significantly extend the duration of the post-impact warm period, and even for cloud coverage significantly lower than predicted in Ramirez and Kasting (2017). However, the range of cloud microphysical properties for which this scenario works is very narrow.Using 2-D Mantle Dynamics simulations we find that large bolide impacts can produce a strong thermal anomaly in the mantle of Mars that can survive and propagate for tens of millions of years. This thermal anomaly could raise the near-surface internal heat flux up to several hundreds of mW/m 2 (i.e. up to ∼ 10 times the ambient flux) for several millions years at the edges of the impact crater. However, such internal heat flux is largely insufficient to keep the martian surface above the melting point of water.In addition to the poor temporal correlation between the formation of the largest basins and valley networks (Fassett and Head, 2011), these arguments indicate that the largest ...