We give an overview of the recent developments on the study of various types of derivations (such as Jordan and Lie derivations) on certain (Banach) algebras‎. ‎In the realm of Jordan derivations the standard problem is to find out conditions under which a Jordan derivation is a derivation; while in the context of Lie derivations the main problem is providing those conditions under which a Lie derivation is proper‎, ‎that is‎, ‎can be decomposed into the sum of a derivation and a center-valued mapping‎. ‎In this talk‎, ‎we are mainly dealing with the study of these problems on some variety of algebras‎, ‎including trivial extensions‎, ‎triangular algebras‎, ‎generalized matrix algebras and $C^*-$algebras

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