Conversational Information Retrieval (CIR) has garnered considerable attention in recent years. A key challenge in CIR is formulating effective queries during the dialogue between the searcher and the conversational agent. Unlike traditional information retrieval systems, where users independently formulate a complete query for each search operation, conversational systems offer the opportunity for agents to assist users in an interactive, multi-turn search process. This alleviates the burden on users to express their full information need in a single query by leveraging the iterative nature of conversation to gradually refine and clarify their search. Conversational context plays a vital role in this query formulation process. In natural language conversations, each turn may implicitly or explicitly refer to previous dialogue turns. This dependency of the turns in the dialogue on conversational history introduces the challenge of identifying and understanding the relevant parts of the dialogue context to correctly interpret the current query. This PhD project focuses on understanding and leveraging conversational context from two dimensions: conversational history and user knowledge. Conversational history deals with identifying and exploiting the relevant parts from within the conversational historical context to disambiguate and interpret the query, while Knowledge deals with exploiting user knowledge of the subject as well as that accumulated during the conversation. The goal of this thesis is to study conversational context in CIR, with a focus on understanding and modeling these two dimensions. The contributions of this work are twofold: (1) methods for identifying and modeling relevant portions of the conversational history, and (2) approaches for modeling the evolving knowledge of users throughout the dialogue. These contributions aim to improve the effectiveness and responsiveness of conversational information retrieval systems.