  The development of coalescent theory paved the way to statistical inference
from population genetic data. In the genomic era, however, coalescent models
are limited due to the complexity of the underlying ancestral recombination
graph. The sequentially Markov coalescent (SMC) is a heuristic that enables the
modelling of complete genomes under the coalescent framework. While it empowers
the inference of detailed demographic history of a population from as few as
one diploid genome, current implementations of the SMC make unrealistic
assumptions about the homogeneity of the coalescent process along the genome,
ignoring the intrinsic spatial variability of parameters such as the
recombination rate. Here, I review the historical developments of SMC models
and discuss the evidence for parameter heterogeneity. I then survey approaches
to handle this heterogeneity, focusing on a recently developed extension of the
SMC.
