Conversational search and recommendation based on user-system dialogs exhibit major differences from conventional search and recommendation tasks in that 1) the user and system can interact for multiple semantically coherent rounds on a task through natural language dialog, and 2) it becomes possible for the system to understand the user needs or to help users clarify their needs by asking appropriate questions from the users directly. We believe the ability to ask questions so as to actively clarify the user needs is one of the most important advantages of conversational search and recommendation. In this paper, we propose and evaluate a unified conversational search/recommendation framework, in an attempt to make the research problem doable under a standard formalization. Specifically, we propose a System Ask - User Respond (SAUR) paradigm for conversational search, define the major components of the paradigm, and design a unified implementation of the framework for product search and recommendation in e-commerce. To accomplish this, we propose the Multi-Memory Network (MMN) architecture, which can be trained based on large-scale collections of user reviews in e-commerce. The system is capable of asking aspect-based questions in the right order so as to understand the user needs, while (personalized) search is conducted during the conversation, and results are provided when the system feels confident. Experiments on real-world user purchasing data verified the advantages of conversational search and recommendation against conventional search and recommendation algorithms in terms of standard evaluation measures such as NDCG.