<p>The permafrost of the northern hemisphere is degrading due to rising global temperatures. This degradation poses significant threats to buildings and infrastructure in these regions. Due to these potential risks, various mitigation strategies are devised to stabilize the degrading permafrost. One mitigation approach includes using shallow geothermal technologies such as heat pumps and thermosyphons for ground cooling. Using these technologies offers several benefits, such as stabilizing permafrost ground, preserving permafrost, and promoting renewable energy use. Preserving permafrost is especially important for mitigating the effects of the permafrost carbon cycle. Therefore, implementing shallow geothermal technologies in infrastructure design can enhance resilience and adaptability to climate change. Hence, understanding ground responses to geothermal operations is crucial. Multiphysics modeling is key in understanding these responses and mitigating geohazards. Despite the multidisciplinary nature of this topic, there is a notable lack of comprehensive reviews. This paper addresses this gap by reviewing the current state of the ground in cold regions, examining shallow geothermal technologies in these areas, and evaluating ground response modeling in the literature to highlight the role of multiphysics models in analyzing ground–geothermal system interactions in cold regions. The gaps and limitations in the literature and potential emerging topics are also discussed.</p>