The macroscopic behaviour of a two-phase foam depends on chemical properties such as surface tension, and physical properties such as the shape and size of the bubbles in the foam. The chemical properties of a foaming material may be deduced from experiments on the material in the single phase, for example surface tension or viscosity measurements. However, in order to measure structure the foam must clearly be present. This presents a difficult problem, especially for liquid foams which are often fast-moving and liable to collapse or rearrange on coming into contact with a probe. Optical techniques for examining foam structures can be non-invasive and take advantage of the semi-transparent nature of many liquid and solid foams. In particular, the application of confocal and axial tomography systems to real three-dimensional cellular foams can resolve their local geometric structure. This thesis covers the application of new optical tomographic techniques to the imaging of foams and presents the first three-dimensional models of bubble structure in liquid and solid foams. Complete descriptions of the hardware and software are included; imaging systems are based on a personal computer with an inexpensive video digitising card and a CCD camera. A clear advantage of optical systems is that the high data bandwidth required for tomography is available even on relatively slow computers by modern standards. Typically, all the data for a sixteen-million (256³) voxel model covering a world volume of 64mm³ can be acquired in a period of 30 seconds. Results from this work include the first three-dimensional solid models of observed foams, both aqueous and polyurethane-based, including volume models of minimal energy cellular foam configurations. In particular, Kelvin's proposed minimal cell and also bubbles from the Weaire-Phelan structure have been resolved by the system.