Deep learning-based 3D object detection has achieved unprecedented success with the advent of large-scale autonomous driving datasets. However, drastic performance degradation remains a critical challenge for cross-domain deployment. In addition, existing 3D domain adaptive detection methods often assume prior access to the target domain annotations, which is rarely feasible in the real world. To address this challenge, we study a more realistic setting, unsupervised 3D domain adaptive detection, which only utilizes source domain annotations. 1) We first comprehensively investigate the major underlying factors of the domain gap in 3D detection. Our key insight is that geometric mismatch is the key factor of domain shift. 2) Then, we propose a novel and unified framework, Multi-Level Consistency Network (MLC-Net), which employs a teacher-student paradigm to generate adaptive and reliable pseudo-targets. MLC-Net exploits point-, instance-and neural statistics-level consistency to facilitate cross-domain transfer. Extensive experiments demonstrate that MLC-Net outperforms existing state-of-the-art methods (including those using additional target domain information) on standard benchmarks. Notably, our approach is detector-agnostic, which achieves consistent gains on both single-and two-stage 3D detectors. Code will be released.