Micro-combustion for micro-thermophotovoltaic (MTPV) and micro-thermoelectric (MTE) systems is gaining renewed interest as a pathway toward compact power generation with high energy density. This review examines how emerging artificial intelligence (AI) methodologies can accelerate the development of such systems by addressing longstanding modeling, optimization, and design challenges. We analyze four major research areas: artificial neural network (ANN)-based design optimization, AI-driven prediction of micro-scale flow variables, Physics-Informed Neural Networks for combustion modeling, and surrogate models that approximate high-fidelity computational fluid dynamics (CFD) and detailed chemistry solvers. These approaches enable faster exploration of geometric and operating spaces, improved prediction of nonlinear flow and reaction dynamics, and efficient reconstructions of thermal and chemical fields. The review outlines a wide range of future research directions motivated by advances in high-fidelity modeling, AI-based optimization, and hybrid data-physics learning approaches, while also highlighting key challenges related to data availability, model robustness, validation, and manufacturability. Overall, the synthesis shows that overcoming these limitations will enable the development of micro-combustors with higher energy efficiency, lower emissions, more stable and controllable flames, and the practical realization of commercially viable MTPV and MTE systems.