I will present some observational results illustrating the properties of AGN-driven outflows and their effect on star formation in their host galaxies. In particular I will present multi-band observations
tracing both the molecular and ionized phase of the ISM, both in local and distant galaxies, illustrating that AGNs can drive extremely powerful and energetic outflows, which can expel a large fraction
of the gas in their host galaxies, hence suppressing star formation (negative feedback). However, I will also show evidence that in some cases AGN-driven outflows can actually trigger star formation, both in their host galaxy discs and even in the outflow itself. This is a new mode of star formation, which can contribute significantly to galaxy evolution. I will conclude by presenting the exciting prospects of further investigating these effects in the near future.