This paper presents a novel neural model - Dynamic Fusion Network (DFN), for machine reading comprehension (MRC). DFNs differ from most state-of-the-art models in their use of a dynamic multi-strategy attention process, in which passages, questions and answer candidates are jointly fused into attention vectors, along with a dynamic multi-step reasoning module for generating answers. With the use of reinforcement learning, for each input sample that consists of a question, a passage and a list of candidate answers, an instance of DFN with a sample-specific network architecture can be dynamically constructed by determining what attention strategy to apply and how many reasoning steps to take. Experiments show that DFNs achieve the best result reported on RACE, a challenging MRC dataset that contains real human reading questions in a wide variety of types. A detailed empirical analysis also demonstrates that DFNs can produce attention vectors that summarize information from questions, passages and answer candidates more effectively than other popular MRC models.