In this talk we present recent results regarding bosons featuring a spontaneous pattern formation or led by quasi-periodic shallow lattices. It will be explored an interesting set of quasi-periodic phases headed by genuine quantum properties which, in some cases, manifest a supersolid regime or even a Bose glass behaviour, both observable at finite temperature too. Finally, for quasi-crystalline lattices, we illustrate how those phases result accessibile exploiting values of densities and interaction strengths comparable with those used in state-of-the-art experimental setups with ultra-cold atoms.