With the highly dense genomic data available nowadays, ignoring linkage between genes would result in a huge loss of information. One way to prevent such a loss is to focus on the blocks of chromosomes shared identical by descent (IBD) in populations. The development of the theoretical framework modelling IBD processes is essential to support the advent of new tools such as haplotype phasing, imputation, inferring population structure and demographic history, mapping loci or detecting signatures of selection. This article aims to present the relevant models used in this context, and specify the underlying definitions of identity by descent that are yet to be gathered at one place. In light of this, we derived a general expression for the expected IBD block length, for any population model at any generation after founding.