In this talk we consider various versions of Ramsey-type questions in a random graph setting: the classical Ramsey problem, anti-Ramsey questions, Maker-Breaker games. It is easy to see that one should expect the same threshold (namely, the m2-density of the forbidden graph F) for all these problems. The aim of this talk is to provide a general framework for proving 0-statements and to then apply it to the three problems mentioned above. We also provide an extension to hypergraphs.