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This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra $𝔽S_n$ of the symmetric group $S_n$ over a field $𝔽$ of characteristic 0 (or $p>n$). The goal is to obtain a constructive version of the isomorphism $\psi :{⨁}_{\lambda }{M}_{d_{\lambda }}\left(𝔽\right)⟶𝔽S_n$ where $\lambda$ is a partition of $n$ and $d_{\lambda }$ counts the standard tableaux of shape $\lambda$....