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Recommender systems have become crucial in information filtering nowadays. Existing recommender systems extract user preferences based on the correlation in data, such as behavioral correlation in collaborative filtering, feature-feature, or feature-behavior correlation in click-through rate prediction. However, unfortunately, the real world is driven by causality, not just correlation, and correlation does not imply causation. For instance, recommender systems might recommend a battery charger to a user after buying a phone, where the latter can serve as the cause of the former; such a causal relation cannot be reversed. Recently, to address this, researchers in recommender systems have begun utilizing causal inference to extract causality, thereby enhancing the recommender system. In this survey, we offer a comprehensive review of the literature on causal inference-based recommendation. Initially, we introduce the fundamental concepts of both recommender system and causal inference as the foundation for subsequent content. We then highlight the typical issues faced by non-causality recommender system. Following that, we thoroughly review the existing work on causal inference-based recommender systems, based on a taxonomy of three-aspect challenges that causal inference can address. Finally, we discuss the open problems in this critical research area and suggest important potential future works.