We present a modern hierarchical classification of metaheuristic algorithms based on assigning each metaheuristic to a single class within a system of mutually exclusive and non-overlapping classes. For each metaheuristic, there are specific tasks that it is good at handling. An example of classification is considered. Current approaches to testing metaheuristics are presented: discrete and continuous optimization problems, as well as optimization problems. The tendency to compare the performance of metaheuristics using statistical hypothesis testing on benchmarks is noted. The problems successfully solved by metaheuristics in such fields as engineering design, image processing and computer vision, computer networks and communications, energy and energy management, data analysis and machine learning, medicine and transportation are systematized. Optimization problems requiring further research are highlighted: dynamic and stochastic optimization problems; multicriteria optimization problems; multimodal optimization problems; multidimensional optimization problems; memetic optimization problems in which many search algorithms are combined; as well as optimization problems and adaptation of metaheuristics parameter settings to achieve a balance between convergence speed and diversification of the solution search space.