The character of the finite-dimensional irreducible modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible modules over classical Lie superalgebras.

In this talk, we give a brief review on classical results and then introduce an analogous conjectural character formula for finite-dimensional irreducible modules over classical Lie superalgebras, often referred to as Kac-Wakimoto formula, together with our recent work on the proof for the case of ortho-symplectic Lie superalgebras.