Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we intend to provide an overview of convergence and efficiency studies of metaheuristics, and try to provide a framework for analyzing metaheuristics in terms of convergence and efficiency. This can form a basis for analyzing other algorithms. We also outline some open questions as further research topics.