Epigenetic regulation is a fundamental component of biological organization, governing how genetically identical cells develop and maintain distinct behavior in response to the same external stimuli. Understanding how these mechanisms evolve has therefore become a central question in developmental biology, immunology, and oncology. Starting from a biological overview of epigenetics and its significance, we explore how different modeling paradigms—from discrete to continuum—represent cell and epigenetic evolution. When a continuum epigenetic spectrum is considered, two main strategies are used. In the first, the physical space is expanded with additional epigenetic dimensions that describe the phenotypic space. Cells evolve in time through reaction-diffusion equations, occupying subsequent positions within that extended space, similar to standard Eulerian formulations in Continuum Physics. The second defines the epigenetic state by a set of internal variables carried by each cell representative volume that now evolves along time trajectories. This strategy may be interpreted as discretizing the epigenetic state continuous representation into a few variables whose evolution is tracked along time.
In this work, we present these two approaches and formulate them under both Eulerian and Lagrangian viewpoints, focusing first on cellular evolution and subsequently extending the framework to include adaptation and phenotypic plasticity. Building upon this general framework, we review and discuss various procedures found in the literature for modeling epigenetic changes in cell populations. This comparative analysis establishes a coherent foundation for hybrid (discrete-continuous phenotypes) and multiscale models, while elucidating the fundamental differences between existing modeling frameworks.