In this talk we present both classical and recent results in the representation theory of Jordan superalgebras. Further we will construct indecomposable representations of Kantor superalgebra $Kan(n)$, $n\geq 1$ and of Jordan superalgebra $JP_2$. Our main tool is the famous Tits-Kantor-Koecher construction. The representations of Jordan superalgebras $J$ are given in terms of Ext quiver algebras of the category of representations with the short grading for $TKK(J)$.
This is joint result with Vera Serganova.