Conversational search is an embodiment of an iterative and interactive approach to information retrieval (IR) that has been studied for decades. Due to the recent rise of intelligent personal assistants, such as Siri, Alexa, AliMe, Cortana, and Google Assistant, a growing part of the population is moving their information-seeking activities to voice- or text-based conversational interfaces. One of the major challenges of conversational search is to leverage the conversation history to understand and fulfill the users\u27 information needs. In this dissertation work, we investigate history modeling approaches for conversational information retrieval. We start from history modeling for user intent prediction. We analyze information-seeking conversations by user intent distribution, co-occurrence, and flow patterns, followed by a study of user intent prediction in an information-seeking setting with both feature-based methods and deep learning methods. We then move to history modeling for conversational question answering (ConvQA), which can be considered as a simplified setting of conversational search. We first propose a positional history answer embedding (PosHAE) method to seamlessly integrate conversation history into a ConvQA model based on BERT. We then build upon this method and design a history attention mechanism (HAM) to conduct a ``soft selection\u27\u27 for conversation history. After this, we extend the previous ConvQA task to an open-retrieval (ORConvQA) setting to emphasize the fundamental role of retrieval in conversational search. In this setting, we learn to retrieve evidence from a large collection before extracting answers. We build an end-to-end system for ORConvQA, featuring a learnable dense retriever. We conduct experiments with both fully-supervised and weakly-supervised approaches to tackle the training challenges of ORConvQA. Finally, we study history modeling for conversational re-ranking. Given a history of user feedback behaviors, such as issuing a query, clicking a document, and skipping a document, we propose to introduce behavior awareness to a neural ranker. Our experimental results show that the history modeling approaches proposed in this dissertation can effectively improve the performance of different conversation tasks and provide new insights into conversational information retrieval
