The aim of this study was exploration of the genetic background of conjunctival melanoma (CM) and correlation with recurrent and metastatic disease. Twenty-eight CM from the Rotterdam Ocular Melanoma Study group were collected and DNA was isolated from the formalin-fixed paraffin embedded tissue. Targeted next-generation sequencing was performed using a panel covering GNAQ, GNA11, EIF1AX, BAP1, BRAF, NRAS, c-KIT, PTEN, SF3B1, and TERT genes. Recurrences and metastasis were present in eight (29%) and nine (32%) CM cases, respectively. TERT promoter mutations were most common (54%), but BRAF (46%), NRAS (21%), BAP1 (18%), PTEN (14%), c-KIT (7%), and SF3B1 (4%) mutations were also observed. No mutations in GNAQ, GNA11, and EIF1AX were found. None of the mutations was significantly associated with recurrent disease. Presence of a TERT promoter mutation was associated with metastatic disease (p-value = 0.008). Based on our molecular findings, CM comprises a separate entity within melanoma, although there are overlapping molecular features with uveal melanoma, such as the presence of BAP1 and SF3B1 mutations. This warrants careful interpretation of molecular data, in the light of clinical findings. About three quarter of CM contain drug-targetable mutations, and TERT promoter mutations are correlated to metastatic disease in CM.