People often encounter troubles in everyday conversations, prompting them to initiate repairs, which are various approaches employed to recognize and resolve those problems, fostering mutual understanding across conversational turns. However, maintaining a smooth interaction remains challenging for Conversational Agents (CAs), which are dialogue systems designed to simulate conversation with humans (including chatbots, social robots, and virtual assistants). To foster seamless human-agent interaction, the CA should be able to recognize repairs initiated by humans, utilize multimodal cues, and participate in the repair process. This article, which is an overview of our thesis research project, outlines our ongoing efforts to accomplish this objective. The initial phase involves analyzing repair phenomena in human-human interactions.