Title: Iterative Memory Network for Long Sequential User Behavior Modeling in Recommender Systems. Abstract: Sequential user behavior modeling is a key feature in modern recommender systems, seeking to capture users' interest based on their past activities. There are two usual approaches to sequential modeling : Recurrent Neural Networks (RNNs) and the attention mechanism. As the user behavior sequence gets longer, the usual approaches encounter problems. RNN-based methods incur the problem of fast forgetting, making it difficult to model the user's interests long time ago. The self-attention mechanism and its variations such as the transformer structure have the unfortunate property of a quadratic cost with respect to the input length, which makes it difficult to deal with long inputs. The target attention mechanism, despite having only $O(L)$ memory and time complexity, cannot model intra-sequence dependencies. In this paper, we propose Iterative Memory Network (IMN), an end-to-end differentiable framework for long sequential user behavior modeling. In our model, the target item acts as a memory trigger, continuously eliciting relevant information from the long sequence to represent the user's memory on the particular target item. In the Iterative Memory Update module, the model walks over the long sequence multiple iterations and keeps a memory vector to memorize the content walked over. Within each iteration, the sequence interacts with both the target item and the current memory for both target-sequence relation modeling and intra-sequence relation modeling. The memory is updated after each iteration. The framework incurs only $O(L)$ memory and time complexity while reduces the maximum length of network signal travelling paths to $O(1)$, which is achieved by the self-attention mechanism with $O(L^2)$ complexity. Various designs of efficient self-attention mechanisms are at best $O(LlogL)$. Extensive empirical studies show that our method outperforms various state-of-the-art sequential modeling methods on both public and industrial datasets for long sequential user behavior modeling. 