The classical Diffie Hellman key exchange protocol can be generalized by using an action of an Abelian semigroup on a set. Its security is based on the assumed hardness of the analog to the Discrete Log Problem, which we call Semigroup Action Problem (SAP). I will present various examples of such semigroup actions and discuss their security. Also I will introduce an important ingredient to build some promising semigroup actions, the so-called congruence-free (or simple) semirings.