Traditional information retrieval applications require users to develop a well-formed query describing their information need. This places a cognitive burden on the searcher who must expend effort in attempting to select words that succinctly describe their information need, with the implicit assumption that they know enough to describe their target. A more natural mode of human enquiry is via dialogues which enable incremental development of topical understanding and corresponding effective queries. The conversational search seeks to enable the next generation of more natural and efficient search applications that should be easy to use while less cognitively demanding on searchers. Since conversation is a natural means of human information inquiry, framing the information retrieval process within dialogue is hypothesized to make the search process more natural for the user in terms of query entry, interaction to locate relevant content, and engaging with system output. This PhD research project seeks to make progress toward realizing the vision of conversational search systems. In this project, we investigate the opportunities to integrate the exploratory search process within a conversational setting. We propose a conceptual framework for dialogue-based exploratory search applications combining a standard search tool with an interactive agent in an integrated user interface. Additionally, we introduce an implicit evaluation framework for conversational search in exploratory search setting, including multiple dimensions: search experience, knowledge gain, software usability, cognitive load and user experience, based on studies of conversational systems and information retrieval. We examine the behaviour of current conversational assistants to support complex information seeking tasks and propose and evaluate extensions to improve their effectiveness. Using implicit evaluation we examine the user-experience using our conversational search interface using a conversational agent taking a rule-based approach and a machine learning approach. Our findings show that users respond intuitively and positively to the introduction of conversational support into their interactive search experience.