Multi-agent path finding (MAPF) attracts considerable attention in artificial intelligence community. The task in the standard MAPF is to find discrete paths through which agents can navigate from their starting positions to individual goal positions. The combination of two additional requirements makes the problem computationally challenging: agents must not collide with each other and the paths must be optimal with respect to some objective. Two major approaches to optimal MAPF solving include dedicated search-based methods, and compilation-based methods that reduce a MAPF instance to an instance in a different formalism, for which an efficient solver exists. In this survey, we summarize major compilation-based solvers for MAPF using CSP, SAT, and MILP formalisms. We explain the core ideas of the solvers in a simplified and unified way while preserving the merit making them more accessible for a wider audience.