Conversational agents (CAs) are software designed to respond to user questions with natural language. These agents are employed in various domains, such as education, healthcare, customer service, and team collaboration, to assist individuals in their daily tasks. Recent advances in natural language processing and artificial intelligence have significantly enhanced the quality of interactions between these agents and humans. Consequently, designers are now focusing on creating agents with diverse characteristics, specifically anthropomorphic designs, to better meet user needs and preferences, moving away from a'one size fits all'approach. Despite the growing interest and various approaches in academia and practice to measure user perceptions of these designs, there remains a need for a comprehensive understanding of the current state of CA design research. To address this issue, we systematically reviewed 40 studies related to CA design from the Information Systems (IS) and Human-Computer Interaction (HCI) conferences. We examined the methodologies used in design research, types of agents, and communication modes and mapped user perceptions with the agents. Our analysis highlights that while text-based agents, particularly chatbots, predominate, they might utilize diverse designs such as communication patterns, verbal expressiveness, greetings, self-references, and polite phrases, for example, to enhance service satisfaction, perceived empathy, and competency. Voice-based agents significantly improve learning outcomes and engagement in educational contexts through gestures and voices. Most studies utilize laboratory and online experiments, which effectively capture user responses and provide insights into the immediate impacts of CAs on user perceptions. On the basis of these findings, our study provides a comprehensive overview of the status quo of CA design research, identifies the key dimensions of user perception and outcomes, and offers guidance for future research.