The explosion in the amount of information that is being processed is prompting the need for new computing systems beyond existing electronic computers. Photonic computing is emerging as an attractive alternative due to performing calculations at the speed of light, the change for massive parallelism, and also extremely low energy consumption. We review the physical implementation of basic optical calculations, such as differentiation and integration, using metamaterials, and introduce the realization of all-optical artificial neural networks. We start with concise introductions of the mathematical principles behind such optical computation methods and present the advantages, current problems that need to be overcome, and the potential future directions in the field. We expect that our review will be useful for both novice and experienced researchers in the field of all-optical computing platforms using metamaterials.