Automated quantitative estimation of spinal curvature is an important task for the ongoing evaluation and treatment planning of Adolescent Idiopathic Scoliosis (AIS). It solves the widely accepted disadvantage of manual Cobb angle measurement (time-consuming and unreliable) which is currently the gold standard for AIS assessment. Attempts have been made to improve the reliability of automated Cobb angle estimation. However, it is very challenging to achieve accurate and robust estimation of Cobb angles due to the need for correctly identifying all the required vertebrae in both Anterior-posterior (AP) and Lateral (LAT) view x-rays. The challenge is especially evident in LAT x-ray where occlusion of vertebrae by the ribcage occurs. We therefore propose a novel Multi-View Correlation Network (MVC-Net) architecture that can provide a fully automated end-to-end framework for spinal curvature estimation in multi-view (both AP and LAT) x-rays. The proposed MVC-Net uses our newly designed multi-view convolution layers to incorporate joint features of multi-view x-rays, which allows the network to mitigate the occlusion problem by utilizing the structural dependencies of the two views. The MVC-Net consists of three closely-linked components: (1) a series of X-modules for joint representation of spinal structure (2) a Spinal Landmark Estimator network for robust spinal landmark estimation, and (3) a Cobb Angle Estimator network for accurate Cobb Angles estimation. By utilizing an iterative multi-task training algorithm to train the Spinal Landmark Estimator and Cobb Angle Estimator in tandem, the MVC-Net leverages the multi-task relationship between landmark and angle estimation to reliably detect all the required vertebrae for accurate Cobb angles estimation. Experimental results on 526 x-ray images from 154 patients show an impressive 4.04° Circular Mean Absolute Error (CMAE) in AP Cobb angle and 4.07° CMAE in LAT Cobb angle estimation, which demonstrates the MVC-Net's capability of robust and accurate estimation of Cobb angles in multi-view x-rays. Our method therefore provides clinicians with a framework for efficient, accurate, and reliable estimation of spinal curvature for comprehensive AIS assessment.