One of the major discoveries of Stephen Cook is that lower bounds on the lengths of proofs in the propositional calculus can be used to prove independence results. This stimulated research into proving lower bounds for various propositional proof systems. Later it was shown that one can use lower bounds on the size of monotone circuits to prove lower bounds on propositional proofs. New models of monotone computations have been proposed recently that potentially may give us lower bounds for more propositional proof systems that we have so far. In this talk we will survey some results that connect lower bounds on monotone computations in various models with lower bounds on the lengths of proofs in proof systems.