Cryogenics is the science and technology of very low temperatures, typically below 120 K. The most common applications are liquified natural gas carriers, ground-based tanks, and propellant tanks for space launchers. A crucial aspect of cryogenic technology is effective insulation to minimise boil-off from storage tanks and prevent frost build-up. Rigid closed-cell foams are prominent in various applications, including cryogenic insulation, due to their balance between thermal and mechanical properties. Polyurethane (PU) foam is widely used for internal insulation in cryogenic tanks, providing durability under thermal shocks and operational loads. External insulation, used in liquified natural gas carriers and ground-based tanks, generally demands less compressive strength and can utilise lower-density foams. The evolution of cryogenic insulation materials has seen the incorporation of environmentally friendly blowing agents and bio-based polyols to enhance sustainability. Fourth-generation physical blowing agents, such as HFO-1233zd(E) and HFO-1336mzz(Z), offer low global warming potential and improved thermal conductivity. Additionally, bio-based polyols from renewable resources like different natural oils and recycled polyethylene terephthalate (PET) are being integrated into rigid PU foams, showing promising properties for cryogenic applications. Research continues to optimise these materials for better mechanical performance and environmental impact.