Vision-Centric Bird-Eye-View (BEV) perception has shown promising potential and attracted increasing attention in autonomous driving. Recent works mainly focus on improving efficiency or accuracy but neglect the domain shift problem, resulting in severe degradation of transfer performance. With extensive observations, we figure out the significant domain gaps existing in the scene, weather, and day-night changing scenarios and make the first attempt to solve the domain adaption problem for multi-view 3D object detection. Since BEV perception approaches are usually complicated and contain several components, the domain shift accumulation on multi-latent spaces makes BEV domain adaptation challenging. In this paper, we propose a novel Multi-level Multi-space Alignment Teacher-Student ($M^{2}ATS$) framework to ease the domain shift accumulation, which consists of a Depth-Aware Teacher (DAT) and a Multi-space Feature Aligned (MFA) student model. Specifically, DAT model adopts uncertainty guidance to sample reliable depth information in target domain. After constructing domain-invariant BEV perception, it then transfers pixel and instance-level knowledge to student model. To further alleviate the domain shift at the global level, MFA student model is introduced to align task-relevant multi-space features of two domains. To verify the effectiveness of $M^{2}ATS$, we conduct BEV 3D object detection experiments on four cross domain scenarios and achieve state-of-the-art performance (e.g., +12.6% NDS and +9.1% mAP on Day-Night). Code and dataset will be released.