In this talk I shall provide a survey of my recent works and their environs on differential geometry of Lagrangian submanifolds in specific K\"ahler manifolds, such as complex projective spaces, complex space forms, Hermitian symmetric spaces and so on. I shall emphasis on the relationship between certain minimal Lagrangian submanifold in complex hyperquadrics and isoparametric hypersurfaces in spheres. This talk is mainly based on my joint work with Associate Professor Hui Ma (Tsinghua University, Beijing).