Construction of infrastructures in cold regions and the Arctic has grown rapidly since the 2000s, including railways, platforms, bridges, roads, and pipelines. However, the harsh low temperatures significantly influence the mechanical behaviors of construction materials, and bring safety and durability challenges to these engineering structures. This study made a state‐of‐the‐art review on materials and structures exposed to low temperatures. This review started from constructional‐material mechanical properties, including concrete, steel reinforcement, mild/high‐strength steel plate, and steel strand at low temperatures. It reflected that low temperatures improved the strength of construction materials. However, the freeze–thaw cycles (FTCs) had a detrimental effect on the modulus and strength of concrete. Furthermore, it was revealed that low temperatures increased the interfacial bonding strength between the steel reinforcements (or shear connectors) and concrete. Moreover, low temperatures improved the bending, shear, and compression resistances of reinforced concrete (RC) or prestressed concrete structures, but reduced the ductility of RC columns under lateral cyclic loads. Finally, reviews also found that low temperatures improved the compression resistance of concrete‐filled steel tubes using mild, high‐strength, and stainless steels, whereas FTCs and erosion reduced their compression capacity. In addition, low temperatures increased the bending resistance of steel–concrete composite structures, but the FTCs reduced it. The low temperatures bring challenges to the safety and resilience of engineering constructions, which requires careful further studies. Continuous further studies may focus on the durability of materials and the resilience of structures under diverse hazards, including earthquakes, impacts, and even blasts.