Large Language Models (LLMs) are rapidly transforming education by enabling rich conversational learning experiences. This article provides a comprehensive review of how LLM-based conversational agents are being used in higher education, with extensions to secondary and lifelong learning contexts. We synthesize existing literature on LLMs in education and theories of conversational and dialogic pedagogy - including Vygotsky's sociocultural learning (scaffolding and the Zone of Proximal Development), the Socratic method, and Laurillard's conversational framework - and examine how prompting strategies and retrieval-augmented generation (RAG) can align LLM behaviors with these pedagogical theories, and how it can support personalized, adaptive learning. We map educational theories to LLM capabilities, highlighting where LLM-driven dialogue supports established learning principles and where it challenges or falls short of traditional pedagogical assumptions. Notable gaps in applying prior theories to LLMs are identified, such as the models tendency to provide direct answers instead of fostering co-construction of knowledge, and the need to account for the constant availability and broad but non-human expertise of LLM tutors. In response, we propose practical strategies to better align LLM interactions with sound pedagogy - for example, designing prompts that encourage Socratic questioning, scaffolded guidance, and student reflection, as well as integrating retrieval mechanisms to ensure accuracy and contextual relevance. Our aim is to bridge the gap between educational theory and the emerging practice of AI-driven conversational learning, offering insights and tools for making LLM-based dialogues more educationally productive and theory-aligned.