In the last decade, there has been increasing interest in allowing users to understand how the predictions of machine-learned models come about, thus increasing transparency and empowering users to understand and potentially contest those decisions.Dialogue-based approaches, in contrast to traditional one-shot eXplainable Artificial Intelligence (XAI) methods, facilitate interactive, in-depth exploration through multi-turn dialogues, simulating expert conversations. This paper reviews the current state of dialogue-based XAI, presenting a systematic review of 1,339 publications, narrowed down to 14 based on inclusion criteria. We explore theoretical foundations of the systems, propose key dimensions along which different solutions to dialogue-based XAI differ, and identify key use cases, target audiences, system components, and the types of supported queries and responses. Furthermore, we investigate the current paradigms by which systems are evaluated and highlight their key limitations. Key findings include identifying the main use cases, objectives, and audiences targeted by dialogue-based XAI methods, and summarize the main types of questions and information needs. Beyond discussing avenues for future work, we present a meta-architecture for these systems from existing literature and outlined prevalent theoretical frameworks.