Predicting Machine Translation (MT) quality can help in many practical tasks such as MT post-editing. The performance of Quality Estimation (QE) methods has drastically improved recently with the introduction of neural approaches to the problem. However, thus far neural approaches have only been designed for word and sentence-level prediction. We present a neural framework that is able to accommodate neural QE approaches at these fine-grained levels and generalize them to the level of documents. We test the framework with two sentence-level neural QE approaches: a state of the art approach that requires extensive pre-training, and a new light-weight approach that we propose, which employs basic encoders. Our approach is significantly faster and yields performance improvements for a range of document-level quality estimation tasks. To our knowledge, this is the first neural architecture for document-level QE. In addition, for the first time we apply QE models to the output of both statistical and neural MT systems for a series of European languages and highlight the new challenges resulting from the use of neural MT.