<p>Fundamental superalgebras were essentially introduced by Kemer in his proof of the Specht conjecture in characteristic zero. Their key feature is that any finite-dimensional superalgebra satisfies the same identities as a finite direct sum of fundamental superalgebras. The aim of this paper is to provide an overview of the known results on this kind of algebras, for ordinary algebras and in the presence of additional structures. Furthermore, we prove a characterization of fundamental algebras graded by an abelian group within a class of upper triangular matrices with identifications.</p>