Conjunctival melanoma (CjM) is a rare, primary cancer of the ocular region. Genetic and epigenetic characteristics of conjunctival melanoma have not been completely elucidated yet. Conjunctival melanoma presents similarities with cutaneous melanoma, with substantial differences in the biological behavior. We reviewed the genetic and epigenetic insights of CjM involved in invasion and metastatic spread. CjM is commonly characterized by mutations of v-raf murine sarcoma viral oncogene homolog B1 (BRAF), neurofibromin 1 (NF1) and telomerase reverse transcriptase (TERT), high expression of mammalian target of rapamycin (mTOR) and heat shock protein 90 (HSP90), frequent phosphatase and tensin homolog (PTEN) loss and upregulation of specific miRNAs. These features should identify CjM as a distinct subset of melanoma with its own profile, which is more similar to cutaneous melanoma than mucosal melanoma and remarkably different from uveal melanoma.