Real human language mechanisms and the artificial intelligent language processing methods are two independent systems. Exploring the relationship between the two can help develop human-like language models and is also beneficial to reveal the neuroscience of the reading brain. The flourishing research in this interdisciplinal research field calls for surveys to systemically study and analyze the recent successes. However, such a comprehensive review still cannot be found, which motivates our work. This article first briefly introduces the interdisciplinal research progress, then systematically discusses the task of brain decoding from the perspective of simple concepts and complete sentences, and also describes main limitations in this field and put forward with possible solutions. Finally, we conclude this survey with certain open research questions that will stimulate further studies.