We present an interactive approach for inking, which is the process of turning a pencil rough sketch into a clean line drawing. The approach, which we call the Smart Inker, consists of several "smart" tools that intuitively react to user input, while guided by the input rough sketch, to efficiently and naturally connect lines, erase shading, and fine-tune the line drawing output. Our approach is data-driven: the tools are based on fully convolutional networks, which we train to exploit both the user edits and inaccurate rough sketch to produce accurate line drawings, allowing high-performance interactive editing in real-time on a variety of challenging rough sketch images. For the training of the tools, we developed two key techniques: one is the creation of training data by simulation of vague and quick user edits; the other is a line normalization based on learning from vector data. These techniques, in combination with our sketch-specific data augmentation, allow us to train the tools on heterogeneous data without actual user interaction. We validate our approach with an in-depth user study, comparing it with professional illustration software, and show that our approach is able to reduce inking time by a factor of 1.8x while improving the results of amateur users.