From Siri to Alexa to Cortana, conversational interfaces are hitting the mainstream and becoming ubiquitous in our daily lives. However, user experiences with such applications remain disappointing. Although it is easy to get a system to produce words, none of the current agents or bots display general conversational competence. Modeling natural conversation is still a hard problem. But in order to tackle it, conversational UX designers must possess a technical understanding of the structures of natural conversation. This workshop explores the intersection of user interface design and the design of natural conversation. It seeks to outline principles and guidelines for Conversational UX Design as a distinct discipline. Workshop participants will get their hands dirty building conversation flows.