A group of algorithms used to solve NP-hard problems is called metaheuristic and hyper-heuristic algorithms. Problems that have a large number of answers and it takes a long time to find the best one is called NP-hard. The use of metaheuristic & hyper-heuristic algorithms in solving difficult problems results in acceptable answers in a short time. These methods fall into the category of optimization algorithms. In optimization algorithms, problems that do not have a definite solution reach an optimal answer in a very short time. Various algorithms have been introduced so far that stem from the intelligence of the events around us. Each of these methods has been used to solve complex problems that have not received an acceptable response by heuristic algorithms. According to National Football League (NFL) theory, none of the algorithms can solve all the problems. Each of these algorithms achieves more optimal answers to specific problems than the other algorithms. For this reason, efforts to design new methods continue to address a broader range of issues. This article examines new metaheuristic algorithms and their classification. Many metaheuristic algorithms have been introduced today, each of which has the potential to achieve an optimal solution to specific problems. This potential, along with new techniques and Machine Learning (ML), has led to the production of a new generation of these algorithms, known as hyper-heuristic algorithms. These types of algorithms try to produce hybrid algorithms to solve more problems with one algorithm.