In this chapter, we present statistical methods for mapping quantitative-trait loci (QTLs) in outbred or complex pedigrees. Such pedigrees exist primarily in livestock populations, also in human populations, and occasionally in experimental animal or plant populations. The main focus of this chapter is on linkage mapping, but methods for linkage disequilibrium (LD) and combined linkage/LD mapping are also discussed. We describe least-squares and maximum likelihood (ML) methods for estimating QTL effects, and variance-components analysis by approximate (residual) ML for estimating QTL variance contributions. We describe Bayesian QTL mapping, its prior distributions and other distributional assumptions, its implementation via Markov chain Monte Carlo (MCMC) algorithms, its inferences, and contrast it with frequentist methodology. Genotype sampling algorithms using genotypic peeling, allelic peeling or descent graphs are described. Genotype samplers are a critical component of MCMC algorithms implementing ML and Bayesian analyses for complex pedigrees. Lastly, fine-mapping methods including chromosome dissection and LD mapping using current and historical recombinations, respectively, are outlined, and recently developed methods for joint LD and linkage mapping of disease genes and QTL are discussed. INTRODUCTIONIn this chapter, the focus is on statistical methods for mapping of quantitative-trait loci (QTLs) in populations which have not been formed recently by line crossing, and which have pedigree information available over multiple generations. Methods suitable for QTL mapping in (inbred) line crosses are described in Chapter 18. Pedigrees are used for QTL mapping in livestock and human populations, where the development and crossing of inbred lines is not feasible. Therefore, the methods discussed here have applications primarily in mapping genes for quantitative traits of economic importance in livestock and complex disease risk factors in humans. Examples include milk production in dairy 623 Handbook of Statistical Genetics, Third Edition . E dited by D . J. Balding, M . Bishop and C. Cannings.