End-to-end neural Natural Language Processing (NLP) models are notoriously difficult to understand. This has given rise to numerous efforts towards model explainability in recent years. One desideratum of model explanation is faithfulness, i.e. an explanation should accurately represent the reasoning process behind the model's prediction. In this survey, we review over 110 model explanation methods in NLP through the lens of faithfulness. We first discuss the definition and evaluation of faithfulness, as well as its significance for explainability. We then introduce recent advances in faithful explanation, grouping existing approaches into five categories: similarity-based methods, analysis of model-internal structures, backpropagation-based methods, counterfactual intervention, and self-explanatory models. For each category, we synthesize its representative studies, strengths, and weaknesses. Finally, we summarize their common virtues and remaining challenges, and reflect on future work directions towards faithful explainability in NLP.