Uveal melanoma (UM) is the most common intraocular malignant tumor and the most frequent melanoma not affecting the skin. While the rate of UM occurrence is relatively low, about 50% of patients develop metastasis, primarily to the liver, with lethal outcome despite medical treatment. Notwithstanding that UM etiopathogenesis is still under investigation, a set of known mutations and chromosomal aberrations are associated with its pathogenesis and have a relevant prognostic value. The most frequently mutated genes are BAP1, EIF1AX, GNA11, GNAQ, and SF3B1, with mutually exclusive mutations occurring in GNAQ and GNA11, and almost mutually exclusive ones in BAP1 and SF3B1, and BAP1 and EIF1AX. Among chromosomal aberrations, monosomy of chromosome 3 is the most frequent, followed by gain of chromosome 8q, and full or partial loss of chromosomes 1 and 6. In addition, epigenetic mechanisms regulated by non-coding RNAs (ncRNA), namely microRNAs and long non-coding RNAs, have also been investigated. Several papers investigating the role of ncRNAs in UM have reported that their dysregulated expression affects cancer-related processes in both in vitro and in vivo models. This review will summarize current findings about genetic mutations, chromosomal aberrations, and ncRNA dysregulation establishing UM biology.