Since the emergence of conversational agents, this technology has seen continuous development and research. Today, advanced conversational agents are virtually omnipresent in our everyday lives. Albeit the numerous improvements in their conversational capabilities, breakdowns are still a persistent issue. Such breakdowns can result in a very unpleasant experience for users and impair the future success of conversational agents. This issue has been acknowledged by many researchers recently. However, the research on strategies to overcome conversational breakdowns is still inconclusive, and further research is needed. Therefore, we conduct a systematic literature analysis to derive conceptual conversational breakdown recovery strategies from literature and highlight future research avenues to address potential gaps. Thus, we contribute to theory of human-agent interaction by deriving and assessing recovery strategies and suggesting leads for novel recovery strategies.