In this talk, we report our work on the large scale geometric study of Banach-Lie groups, especially of linear Banach-Lie groups. We show that the exponential length, originally introduced by Ringrose for unitary groups of $C^*$-algebras, defines the quasi-isometry type of any connected Banach-Lie group. We also give an affirmative answer to Rosendal's question regarding the existence of a minimal metric for connected Banach-Lie groups. This is a joint work with Michal Doucha (Czech Academy of Sciences), and it is an extension of our previous work with Doucha and Yasumichi Matsuzawa (Shinshu University).