Individual inbreeding coefficient (F) and pairwise relatedness (r) are fundamental parameters in population genetics and have important applications in diverse fields such as human medicine, forensics, plant and animal breeding, conservation and evolutionary biology. Traditionally, both parameters are calculated from pedigrees, but are now increasingly estimated from genetic marker data. Conceptually, a pedigree gives the expected F and r values, FP and rP, with the expectations being taken (hypothetically) over an infinite number of individuals with the same pedigree. In contrast, markers give the realised (actual) F and r values at the particular marker loci of the particular individuals, FM and rM. Both pedigree (FP, rP) and marker (FM, rM) estimates can be used as inferences of genomic inbreeding coefficients FG and genomic relatedness rG, which are the underlying quantities relevant to most applications (such as estimating inbreeding depression and heritability) of F and r. In the pre-genomic era, it was widely accepted that pedigrees are much better than markers in delineating FG and rG, and markers should better be used to validate, amend and construct pedigrees rather than to replace them. Is this still true in the genomic era when genome-wide dense SNPs are available? In this simulation study, I showed that genomic markers can yield much better estimates of FG and rG than pedigrees when they are numerous (say, 10(4) SNPs) under realistic situations (e.g. genome and population sizes). Pedigree estimates are especially poor for species with a small genome, where FG and rG are determined to a large extent by Mendelian segregations and may thus deviate substantially from their expectations (FP and rP). Simulations also confirmed that FM, when estimated from many SNPs, can be much more powerful than FP for detecting inbreeding depression in viability. However, I argue that pedigrees cannot be replaced completely by genomic SNPs, because the former allows for the calculation of more complicated IBD coefficients (involving more than 2 individuals, more than one locus, and more than 2 genes at a locus) for which the latter may have reduced capacity or limited power, and because the former has social and other significance for remote relationships which have little genetic significance and cannot be inferred reliably from markers.