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Abstract Modal Kleene algebras are Kleene algebras with forward and backward modal operators, defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various popular calculi and allows treating quite a number of areas. We survey the basic theory and some prominent applications. These include, on the system semantics side, wlp and wp calculus, PDL (Propositional Dynamic Logic), predicate transformer semantics, temporal logics and termination analysis of rewrite systems and state transition systems. On the derivation side we apply the framework to game analysis and greedy-like algorithms.