Large pedigrees contain a wealth of information about the genetic history of a population. For pedigrees containing thousands to millions of individuals, such as the province-wide pedigree that exists in Quebec, Canada, the joint analysis of genetic and pedigree data is numerically challenging. We introduce a suite of tools for the joint modelling of genetic and pedigree data, and then apply these tools to several problems in large-scale population genetics. We will discuss four applications: 1-Inference of disease history through tracking of ancestral carriers; 2-Modelling of long-range linkage induced by fine-scale population structure, 3-Reconstruction of missing pedigree information, 4-Optimal sampling strategies for building large haplotype panels in spatially inhomogeneous populations. We will discuss applications based on the BALSAC genealogical database, recessive diseases in the French-Canadian population, and genome-wide association studies.