Recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics are reviewed: modelling allelic association and pedigree based linkage analysis. Estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility, are described and illustrated. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.