Genetic interactions or epistasis have been thought to play a pivotal role in shaping the formation, development and evolution of life. Previous work focused on lower-order interactions between a pair of genes, but it is obviously inadequate to explain a complex network of genetic interactions and pathways. We review and assess a statistical model for characterizing high-order epistasis among more than two genes or quantitative trait loci (QTLs) that control a complex trait. The model includes a series of start-of-the-art standard procedures for estimating and testing the nature and magnitude of QTL interactions. Results from simulation studies and real data analysis warrant the statistical properties of the model and its usefulness in practice. High-order epistatic mapping will provide a routine procedure for charting a detailed picture of the genetic regulation mechanisms underlying the phenotypic variation of complex traits.