An issue often encountered in statistical genetics is whether, or to what extent, it is possible to estimate the degree in which individuals sampled from a background population are related to each other, on the basis of the available diploid multi-locus genotype data and some information on the demography of that population. In this talk, this question is considered by using an explicit modelling and reconstruction of the pedigrees and gene flows at the marker loci. For computational reasons, the analysis is restricted to a relatively recent history of the population, currently extending, depending of the data, up to ten or twenty generations backwards in time. As a computational tool, we use Markov Chain Monte Carlo numerical integration on the state space of genealogies of the sample individuals. The main technical challenge has been in devising a variety of joint proposal distributions which would guarantee that the algorithm has reasonable mixing properties. As illustrations of the method, we consider the question of relatedness both in terms of individuals (pedigree based relatedness estimation) and at the level of genes/genomes (IBD-estimation), using both simulated and real data.