Angiogenesis, the formation of new blood vessels from pre-existing ones, is a crucial process in the progression and metastasis of melanoma. Recent research has highlighted the significant role of epigenetic modifications in regulating angiogenesis. This review comprehensively examines the current understanding of how epigenetic mechanisms, including DNA methylation, histone modifications, and non-coding RNAs, influence angiogenic pathways in melanoma. DNA methylation, a key epigenetic modification, can silence angiogenesis inhibitors such as thrombospondin-1 and TIMP3 while promoting pro-angiogenic factors like vascular endothelial growth factor (VEGF). Histone modifications, including methylation and acetylation, also play a pivotal role in regulating the expression of angiogenesis-related genes. For instance, the acetylation of histones H3 and H4 is associated with the upregulation of pro-angiogenic genes, whereas histone methylation patterns can either enhance or repress angiogenic signals, depending on the specific histone mark and context. Non-coding RNAs, particularly microRNAs (miRNAs) further modulate angiogenesis. miRNAs, such as miR-210, have been identified as key regulators, with miR-9 promoting angiogenesis by targeting E-cadherin and enhancing the expression of VEGF. This review also discusses the therapeutic potential of targeting epigenetic modifications to inhibit angiogenesis in melanoma. Epigenetic drugs, such as DNA methyltransferase inhibitors (e.g., 5-azacytidine) and histone deacetylase inhibitors (e.g., Vorinostat), have shown promise in preclinical models by reactivating angiogenesis inhibitors and downregulating pro-angiogenic factors. Moreover, the modulation of miRNAs and lncRNAs presents a novel approach for anti-angiogenic therapy.