Although digital signal processors have been widely used to perform complex computing tasks, they still suffer from some limitations, including the complexity, low speed, and high-power consumption caused by ex pensive analog-to-digital converters. For this reason, there has recently been a strong interest in wave-based analog computing, which avoids analog-to-digital conversion and can perform massively parallel operations, especially based on artificially designed metamaterials. A new analog computing scheme based on sound waves has been proposed. This computing system, called computational metamaterials, can be as fast as the wave speed and as small as the wavelength. It can perform complex mathematical operations on incoming wave packets, and can even perform calculations on integral and differential equations. These functions are expected to realize a new generation of ultra-fast, compact and efficient computing hardware based on sound wave propagation. The development of acoustic computing meta materials has gone from the computation of a single mathematical operation, the tunable design and computing circuit and computational network that integrate multiple computing blocks, to the topological insulator computational metamaterial proposed for the robustness of computation. The computation of a single mathematical operation can be divided into space and time domain. The difference of main design principles is dimension of time and space. The spatial acoustic computational metamaterials mainly require the realization of spatial distribution of Green's function of required calculation in materials. And the time-domain acoustic computational metamaterial needs to design the frequency spectrum to realize the transfer function. Both the space domain and the time domain acoustic computing metamaterials realize operations, such as integration, derivative, and differential equations. The proposed tunable acoustic computational metamaterials are aimed at the problem that the function of the metamaterials cannot be changed while the structure is fixed. By introducing tunable parameters into the metamaterial, it realizes the integration of integral, derivative and other functions on the same metamaterial. The proposal of acoustic metamaterial calculation circuit and calculation network has raised the complexity of metamaterial calculation by another dimension. By introducing the design of acoustic circuit components, such as acoustic switches, the sound waves are controlled to propagate in different circuits, and complex operations, such as series and parallel connection of multiple different metamaterial blocks are realized. Acoustic metamaterial computing network combines the design ideas of acoustic holography and convolutional neural network (CNN). Each pixel unit of the metamaterial is equivalent to a neuron in the CNN, and tlx propagation of sound waves between different metamaterial layers in tlx medium is equivalent to the signal propagation between neurons in different layers. Through training and learning, machine learning tasks, such as handwritten number recognition, have been completed. In view of the computational robustness, the proposed topological insulator computational metamaterials, by introducing the boundary mode of topological protection, ensure that the acoustic computational meta materials can still guarantee the accuracy of the calculation even when the structure parameter is disturbed. In the future, the research of nonlinear computational metamaterials will receive more and more attention, and it will be possible to apply to the fields of nonlinear equation solving, nonlinear filtering, image processing methods and so on. In this review, we discussed the latest developments in the field of acoustic computational metamaterials and studied the latest superstructures used to perform analog computing. We further introduced the applications of acoustic computational metamaterials, including image processing, edge detection, equation solving, and machine learning. Finally, we look forward to key research issues and possible future directions.
