Empirical models of sequence evolution have spurred progress in the field of evolutionary genetics for decades. We are now realizing the importance and complexity of the eukaryotic epigenome. While epigenome analysis has been applied to genomes from single-cell eukaryotes to human, comparative analyses are still relatively few and computational algorithms to quantify epigenome evolution remain scarce. Accordingly, a quantitative model of epigenome evolution remains to be established. We review here the comparative epigenomics literature and synthesize its overarching themes. We also suggest one mechanism, transcription factor binding site (TFBS) turnover, which relates sequence evolution to epigenetic conservation or divergence. Lastly, we propose a framework for how the field can move forward to build a coherent quantitative model of epigenome evolution.