A multitude of stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of ``reader-writer'' histone modifying enzymes. We introduce a unified modeling framework, the ``Painter model'', describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader-writer processes and long-range spreading mechanisms. A systematic analysis of the model highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. To go beyond the effective 3D description, we study explicit 3D polymer dynamics. Since the physics of long, topologically-constrained polymers may significantly deviate from those of shorter chains, we theoretically investigate the extent of the minimal genomic region that one should consider around a given locus in order to effectively capture the correct dynamical and structural properties of the domain of interest. We show that this minimal size depends on the overall epigenomic context and on the entanglement properties of the long polymer. Finally, we introduce a theoretical framework coupling 3D polymer dynamics and epigeneome regulation by diffusing HMEs, the ``Living painter'' model, that exhibits intriguing properties on the coupling between 3D genome folding and epigenetic spreading, reflecting the scope and extension of the thesis.