Navigation is one of the fundamental features of a autonomous robot. And the ability of long-term navigation with semantic instruction is a `holy grail` goals of intelligent robots. The development of 3D simulation technology provide a large scale of data to simulate the real-world environment. The deep learning proves its ability to robustly learn various embodied navigation tasks. However, deep learning on embodied navigation is still in its infancy due to the unique challenges faced by the navigation exploration and learning from partial observed visual input. Recently, deep learning in embodied navigation has become even thriving, with numerous methods have been proposed to tackle different challenges in this area. To give a promising direction for future research, in this paper, we present a comprehensive review of embodied navigation tasks and the recent progress in deep learning based methods. It includes two major tasks: target-oriented navigation and the instruction-oriented navigation.