Voice-based Conversational Agents (CAs) are increasingly being used by children. Through a review of 38 research papers, this work maps trends, themes, and methods of empirical research on children and CAs in HCI research over the last decade. A thematic analysis of the research found that work in this domain focuses on seven key topics: ascribing human-like qualities to CAs, CAs? support of children?s learning, the use and role of CAs in the home and family context, CAs? support of children?s play, children?s storytelling with CA, issues concerning the collection of information revealed by CAs, and CAs designed for children with differing abilities. Based on our findings, we identify the needs to account for children's intersectional identities and linguistic and cultural diversity and theories from multiple disciples in the design of CAs, develop heuristics for child-centric interaction with CAs, to investigate implications of CAs on social cognition and interpersonal relationships, and to examine and design for multi-party interactions with CAs for different domains and contexts.