In this paper, we propose a novel deep learning framework for anatomy segmentation and automatic landmarking. Specifically, we focus on the challenging problem of mandible segmentation from cone-beam computed tomography (CBCT) scans and identification of 9 anatomical landmarks of the mandible on the geodesic space. The overall approach employs three inter-related steps. In step 1, we propose a deep neural network architecture with carefully designed regularization, and network hyper-parameters to perform image segmentation without the need for data augmentation and complex postprocessing refinement. In step 2, we formulate the landmark localization problem directly on the geodesic space for sparselyspaced anatomical landmarks. In step 3, we propose to use a long short-term memory (LSTM) network to identify closelyspaced landmarks, which is rather difficult to obtain using other standard detection networks. The proposed fully automated method showed superior efficacy compared to the state-of-theart mandible segmentation and landmarking approaches in craniofacial anomalies and diseased states. We used a very challenging CBCT dataset of 50 patients with a high-degree of craniomaxillofacial (CMF) variability that is realistic in clinical practice. Complementary to the quantitative analysis, the qualitative visual inspection was conducted for distinct CBCT scans from 250 patients with high anatomical variability. We have also shown feasibility of the proposed work in an independent dataset from MICCAI Head-Neck Challenge (2015) achieving the state-of-the-art performance. Lastly, we present an in-depth analysis of the proposed deep networks with respect to the choice of hyper-parameters such as pooling and activation functions.