Recently, the design of the two-dimensional digital filter has become a subject of interest in the field of two-dimensional signal processing. The two-dimensional digital filter has been applied in many important areas such as image processing, television systems and seismic signal processing. In digital filter design, there are several indispensable aims such as stability, reduced computational complexity and computational time. Thus, researchers and practitioners have investigated various advanced methods based on metaheuristic optimization algorithms for the design of the two-dimensional digital filter. Metaheuristic optimization algorithms have been applied to solve different complicated problems in various fields and they have also been successfully used in digital filter design. This paper presents a review of the design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms such as the genetic algorithm, differential evolution and particle swarm optimization. By comparing the proposed design approaches based on metaheuristic optimization algorithms, it is observed that the genetic algorithm is the most preferred algorithm and emerging novel algorithms using metaheuristic optimization algorithms have better performance in terms of computational complexity and computational time. It is hoped that this review will be helpful for researchers and practitioners studying the design of two-dimensional digital filters.