Low earth orbit (LEO) satellite networks are emerging as important infrastructure for global connectivity and space-based sensing, while their rapidly varying geometry, heterogeneous measurements, and dynamic propagation environments create challenges for acquiring and exploiting spatial radio information. Spectrum cartography provides a framework for constructing and updating spatial representations of radio conditions from sparse observations. This survey reviews learning-based spectrum cartography for LEO satellite networks from an integrated inference--decision perspective. We organize the literature around three representative task categories: radio map reconstruction, localization and state estimation, and map-informed resource allocation. We further examine the progression from classical interpolation, statistical estimation, and structured optimization toward learning-based approaches that exploit environmental context, relational structure, generative modeling, and adaptive information fusion. Particular attention is given to attention mechanisms for learning query- and context-dependent interactions among irregular observations, while distinguishing learned relevance from calibrated measurement reliability. Representative formulations and illustrative examples clarify these modeling principles. Finally, we synthesize cross-cutting lessons and identify open challenges in uncertainty modeling, generalization, dynamic map updating, scalable inference, realistic evaluation, and tighter coupling between radio-map inference and network decision making.

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