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While learning based depth estimation from images/videos has achieved substantial progress, there still exist intrinsic limitations. Supervised methods are limited by a small amount of ground truth or labeled data and unsupervised methods for monocular videos are mostly based on the static scene assumption, not performing well on real world scenarios with the presence of dynamic objects. In this paper, we propose a new learning based method consisting of DepthNet, PoseNet and Region Deformer Networks (RDN) to estimate depth from unconstrained monocular videos without ground truth supervision. The core contribution lies in RDN for proper handling of rigid and non-rigid motions of various objects such as rigidly moving cars and deformable humans. In particular, a deformation based motion representation is proposed to model individual object motion on 2D images. This representation enables our method to be applicable to diverse unconstrained monocular videos. Our method can not only achieve the state-of-the-art results on standard benchmarks KITTI and Cityscapes, but also show promising results on a crowded pedestrian tracking dataset, which demonstrates the effectiveness of the deformation based motion representation. Code and trained models are available at https://github.com/haofeixu/rdn4depth.