Cellular solids are materials made up of cells with solid edges or faces that are piled together to fit a certain space. These materials are already present in nature and have already been utilized in the past. Some examples are wood, cork, sponge and coral. New cellular solids replicating natural ones have been manufactured, such as honeycomb materials and foams, which have a variety of applications because of their special characteristics such as being lightweight, insulation, cushioning and energy absorption derived from the cellular structure. Cellular solids have interesting thermal, physical and mechanical properties in comparison with bulk solids: density, thermal conductivity, Young’s modulus and compressive strength. This huge extension of properties allows for applications that cannot easily be extended to fully dense solids and offers enormous potential for engineering creativity. Their Low densities allow lightweight and rigid components to be designed, such as sandwich panels and large portable and floating structures of all types. Their low thermal conductivity enables cheap and reliable thermal insulation, which can only be improved by expensive vacuum-based methods. Their low stiffness makes the foams ideal for a wide range of applications, such as shock absorbers. Low strengths and large compressive strains make the foams attractive for energy-absorbing applications. In this work, their main properties, applications (real and potential) and recent developments are presented, summarized and discussed.