Delineation of the cardiac structures from 2D echocardiographic images is a common clinical task to establish a diagnosis. Over the past decades, the automation of this task has been the subject of intense research. In this paper, we evaluate how far the state-of-the-art encoder-decoder deep convolutional neural network methods can go at assessing 2D echocardiographic images, i.e. segmenting cardiac structures as well as estimating clinical indices, on a dataset especially designed to answer this objective. We therefore introduce the Cardiac Acquisitions for Multi-structure Ultrasound Segmentation (CA-MUS) dataset, the largest publicly-available and fully-annotated dataset for the purpose of echocardiographic assessment. The dataset contains two and four-chamber acquisitions from 500 patients with reference measurements from one cardiologist on the full dataset and from three cardiologists on a fold of 50 patients. Results show that encoder-decoder based architectures outperform state-of-the-art non-deep learning methods and faithfully reproduce the expert analysis for the end-diastolic and endsystolic left ventricular volumes, with a mean correlation of 0.95 and an absolute mean error of 9.5 ml. Concerning the ejection fraction of the left ventricle, results are more contrasted with a mean correlation coefficient of 0.80 and an absolute mean error of 5.6%. Although these results are below the inter-observer scores, they remain slightly worse than the intra-observer's ones. Based on this observation, areas for improvement are defined, which open the door for accurate and fully-automatic analysis of 2D echocardiographic images.