The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem instance on a case-by-case basis. It has become especially relevant in the last decade, with researchers increasingly investigating how to identify the most suitable existing algorithm for solving a problem instance instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where algorithm selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine algorithm selection systems in practice. The comprehensive classification of approaches identifies and analyses the different directions from which algorithm selection has been approached. This paper contrasts and compares different methods for solving the problem as well as ways of using these solutions.