We present a new large-scale corpus of Question-Answer driven Semantic Role Labeling (QA-SRL) annotations, and the first high-quality QA-SRL parser. Our corpus, QA-SRL Bank 2.0, consists of over 250,000 question-answer pairs for over 64,000 sentences across 3 domains and was gathered with a new crowd-sourcing scheme that we show has high precision and good recall at modest cost. We also present neural models for two QA-SRL subtasks: detecting argument spans for a predicate and generating questions to label the semantic relationship. The best models achieve question accuracy of 82.6\% and span-level accuracy of 77.6\% (under human evaluation) on the full pipelined QA-SRL prediction task. They can also, as we show, be used to gather additional annotations at low cost.