The surge in black-box AI models has prompted the need to explain the internal mechanism and justify their reliability, especially in high-stakes applications, such as healthcare and autonomous driving. Due to the lack of a rigorous definition of explainable AI (XAI), a plethora of research related to explainability, interpretability, and transparency has been developed to explain and analyze the model from various perspectives. Consequently, with an exhaustive list of papers, it becomes challenging to have a comprehensive overview of XAI research from all aspects. Considering the popularity of neural networks in AI research, we narrow our focus to a specific area of XAI research: gradient based explanations, which can be directly adopted for neural network models. In this review, we systematically explore gradient based explanation methods to date and introduce a novel taxonomy to categorize them into four distinct classes. Then, we present the essence of technique details in chronological order and underscore the evolution of algorithms. Next, we introduce both human and quantitative evaluations to measure algorithm performance. More importantly, we demonstrate the general challenges in XAI and specific challenges in gradient based explanations. We hope that this survey can help researchers understand state-of-the-art progress and their corresponding disadvantages, which could spark their interest in addressing these issues in future work.

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