As manipulating images by copy-move, splicing and/or inpainting may lead to misinterpretation of the visual content, detecting these sorts of manipulations is crucial for media forensics. Given the variety of possible attacks on the content, devising a generic method is nontrivial. Current deep learning based methods are promising when training and test data are well aligned, but perform poorly on independent tests. Moreover, due to the absence of authentic test images, their image-level detection specificity is in doubt. The key question is how to design and train a deep neural network capable of learning generalizable features sensitive to manipulations in novel data, whilst specific to prevent false alarms on the authentic. We propose multi-view feature learning to jointly exploit tampering boundary artifacts and the noise view of the input image. As both clues are meant to be semantic-agnostic, the learned features are thus generalizable. For effectively learning from authentic images, we train with multi-scale (pixel / edge / image) supervision. We term the new network MVSS-Net and its enhanced version MVSS-Net++. Experiments are conducted in both within-dataset and cross-dataset scenarios, showing that MVSS-Net++ performs the best, and exhibits better robustness against JPEG compression, Gaussian blur and screenshot based image re-capturing.