Conceived as a general introduction to the book, this chapter is a reminder of the core concepts of genetic mapping and molecular marker-based prediction. It provides an overview of the principles and the evolution of methods for mapping the variation of complex traits, and methods for QTL-based prediction of human disease risk and animal and plant breeding value. The principles of linkage-based and linkage disequilibrium-based QTL mapping methods are described in the context of the simplest, single-marker, methods. Methodological evolutions are analysed in relation with their ability to account for the complexity of the genotype-phenotype relations. Main characteristics of the genetic architecture of complex traits, drawn from QTL mapping works using large populations of unrelated individuals, are presented. Methods combining marker-QTL association data into polygenic risk score that captures part of an individual's susceptibility to complex diseases are reviewed. Principles of best linear mixed model-based prediction of breeding value in animal- and plant-breeding programs using phenotypic and pedigree data, are summarized and methods for moving from BLUP to marker-QTL BLUP are presented. Factors influencing the additional genetic progress achieved by using molecular data and rules for their optimization are discussed.