Coarse-Grained Reconfigurable Architectures (CGRAs) emerged about 30 years ago. The very first CGRAs were programmed manually. Fortunately, some compilation approaches appeared rapidly to automate the mapping process. Numerous surveys on these architectures exist. Other surveys also gather the tools and methods, but none of them focuses on the mapping process only. This paper focuses solely on automated methods and techniques for mapping applications on CGRA and covers the last two decades of research. This paper aims at providing the terminology, the problem formulation, and a classification of existing methods. The paper ends with research challenges and trends for the future.