Deep learning has profoundly transformed remote sensing, yet prevailing architectures like Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) remain constrained by critical trade-offs: CNNs suffer from limited receptive fields, while ViTs grapple with quadratic computational complexity, hindering their scalability for high-resolution remote sensing data. State Space Models (SSMs), particularly the recently proposed Mamba architecture, have emerged as a paradigm-shifting solution, combining linear computational scaling with global context modeling. This survey presents a comprehensive review of Mamba-based methodologies in remote sensing, systematically analyzing about 120 Mamba-based remote sensing studies to construct a holistic taxonomy of innovations and applications. Our contributions are structured across five dimensions: (i) foundational principles of vision Mamba architectures, (ii) micro-architectural advancements such as adaptive scan strategies and hybrid SSM formulations, (iii) macro-architectural integrations, including CNN-Transformer-Mamba hybrids and frequency-domain adaptations, (iv) rigorous benchmarking against state-of-the-art methods in multiple application tasks, such as object detection, semantic segmentation, change detection, etc. and (v) critical analysis of unresolved challenges with actionable future directions. By bridging the gap between SSM theory and remote sensing practice, this survey establishes Mamba as a transformative framework for remote sensing analysis. To our knowledge, this paper is the first systematic review of Mamba architectures in remote sensing. Our work provides a structured foundation for advancing research in remote sensing systems through SSM-based methods. We curate an open-source repository (https://github.com/BaoBao0926/Awesome-Mamba-in-Remote-Sensing) to foster community-driven advancements.