We introduce a neural architecture for navigation in novel environments. Our proposed architecture learns to map from first-person viewpoints and plans a sequence of actions towards goals in the environment. The Cognitive Mapper and Planner (CMP) is based on two key ideas: a) a unified joint architecture for mapping and planning, such that the mapping is driven by the needs of the planner, and b) a spatial memory with the ability to plan given an incomplete set of observations about the world. CMP constructs a top-down belief map of the world and applies a differentiable neural net planner to produce the next action at each time step. The accumulated belief of the world enables the agent to track visited regions of the environment. Our experiments demonstrate that CMP outperforms both reactive strategies and standard memory-based architectures and performs well in novel environments. Furthermore, we show that CMP can also achieve semantically specified goals, such as 'go to a chair'.