Gastroenteropancreatic neuroendocrine neoplasias are a diverse group of neoplasms with different characteristics in terms of site, biological behaviour and metastatic potential. In comparison to other cancers, they are genetically quiet, harbouring relatively few somatic mutations. It is increasingly becoming evident that epigenetic changes are as relevant, if not more so, as somatic mutations in promoting oncogenesis. Despite significant tumour heterogeneity, it is obvious that DNA methylation, histone and chromatin modifications and microRNA expression profiles are distinctive for GEP-NEN subtypes and may correlate with clinical outcome. This review summarises existing knowledge on epigenetic changes, identifying potential contributions to pathogenesis and oncogenesis. In particular, we focus on epigenetic changes pertaining to well-differentiated neuroendocrine tumours, which make up the bulk of NENs. We also highlight both similarities and differences within the subtypes of GEP-NETs and how these relate and compare to other types of cancers. We relate epigenetic understanding to existing treatments and explore how this knowledge may be exploited in the development of novel treatment approaches, such as in theranostics and combining conventional treatment modalities. We consider potential barriers to epigenetic research in GEP-NENs and discuss strategies to optimise research and development of new therapies.