Systems, devices and methods are provided that are related to cellular materials that have a precisely-determined arrangement of voids formed using surface transformation. In various embodiments, the cellular materials are suitable for use in various structural, mechanical and/or thermal applications. One aspect of the present subject matter is a method of forming cellular material. According to various embodiments of the method, a predetermined arrangement of the plurality of holes is formed in a volume of material through a surface of the volume of material. The volume of material is annealed such that the volume of material undergoes a surface transformation in which the arrangement of the plurality of holes is transformed into a predetermined arrangement of at least one empty space below the surface of the volume of material. Other aspects are provided herein.