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.