A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In cases of type I Lie superalgebras or exceptional Lie superalgebras, it is shown that the generalised Jantzen filtration for any genealized Verma module is the unique Loewy filtration,
and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any generalized Verma module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of generalized Verma modules, and in the case of exceptional Lie superalgebras, formulae for characters and dimensions of the finite dimensional simple modules are obtained. This talk is based some joint work with R.B. Zhang.