Radio maps (RMs) provide the digital representation of the wireless propagation environment, mapping complex geographical and topological boundary conditions to critical spatial-spectral metrics that range from received signal strength to full channel state information matrices. The integration of artificial intelligence into next generation wireless networks further necessitates the accurate construction of RMs as a foundational prerequisite for electromagnetic digital twins. This paper presents a comprehensive survey of learning-based RM construction, systematically addressing three intertwined dimensions: data, paradigms, and physics-awareness. From the data perspective, we review physical measurement campaigns, ray tracing simulation engines, and publicly available benchmark datasets, identifying their respective strengths and fundamental limitations. From the paradigm perspective, we establish a core taxonomy that categorizes RM construction into source-aware forward prediction and source agnostic inverse reconstruction, and examine five principal neural architecture families spanning convolutional neural networks, vision transformers, graph neural networks, generative adversarial networks, and diffusion models. We further survey optics-inspired methods adapted from neural radiance fields and 3D Gaussian splatting for continuous wireless radiation field modeling. From the physics-awareness perspective, we introduce a three-level integration framework encompassing data-level feature engineering, loss-level partial differential equation regularization, and architecture level structural isomorphism. Open challenges including foundation model development, physical hallucination detection, and mortized inference for real-time deployment are discussed to outline future research directions. The project page is at https://github.com/UNIC-Lab/Awesome-Radio-Map-Categorized.