  Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms
between the cosets of the subregular $\mathcal{W}$-algebras and the principal
$\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It
can be seen as a variant of Feigin-Frenkel duality between the
$\mathcal{W}_n$-algebras and also as a generalization of the connection between
the $\mathcal{N}=2$ superconformal algebra and the affine algebra
$\hat{\mathfrak{sl}}_{2,k}$.We review the recent developments on the
correspondence of the subregular W-algebras and the principal W-superalgebras
of type A at the level of algebras, modules and intertwining operators,
including fusion rules.
