The emergence of generative AI has accelerated the development of conversational tutoring systems that interact with students through natural language dialogue. Unlike prior intelligent tutoring systems (ITS), which largely function as adaptive and interactive problem sets with feedback and hints, conversational tutors hold the potential to simulate high-quality human tutoring by engaging with students' thoughts, questions, and misconceptions in real time. While some previous ITS, such as AutoTutor, could respond conversationally, they were expensive to author and lacked a full range of conversational ability. Generative AI has changed the capacity of ITS to engage conversationally. However, realizing the full potential of conversational tutors requires careful consideration of what research on human tutoring and ITS has already established, while also unpacking what new research will be needed. This paper synthesizes tenets of successful human tutoring, lessons learned from legacy ITS, and emerging work on conversational AI tutors. We use a keep, change, center, study framework for guiding the design of conversational tutoring. We argue that systems should keep proven methods from prior ITS, such as knowledge tracing and affect detection; change how tutoring is delivered by leveraging generative AI for dynamic content generation and dialogic scaffolding; and center opportunities for meaning-making, student agency, and granular diagnosis of reasoning. Finally, we identify areas requiring further study, including efficacy testing, student experience, and integration with human instruction. By synthesizing insights from human tutoring, legacy ITS, and emerging generative AI technologies, this paper outlines a research agenda for developing conversational tutors that are scalable, pedagogically effective, and responsive to the social and motivational dimensions of learning.

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