In this talk, we will study the associated varieties and Gelfand-Kirillov dimensions of highest weight Harish-Chandra modules for noncompact simple Lie groups. In the first part (joint work with Markus Hunziker), we will give a uniform formula to provide the  AV and GKdim for all  unitary highest weight Harish-Chandra modules. In the second part (joint work with Xun Xie), by using Lusztig's a-function we will give a combinatorial algorithm for the GKdim of all highest weight modules of simple Lie algebras of type A. Finally, we will give a formula which can determine the AV of highest weight Harish-Chandra modules for all types. This part is a joint work with Markus Hunziker and Roger Zierau.