Monolayer group-VIB transition-metal dichalcogenides have recently emerged as a new class of semiconductors in the two-dimensional limit. he atractive properties include the visible range direct band gap ideal for exploring optoelectronic applications; the intriguing physics associated with spin and valley pseudospin of carriers which implies potentials for novel electronics based on these internal degrees of freedom; the exceptionally strong Coulomb interaction due to the two-dimensional geometry and the large efective masses. he physics of excitons, the bound states of electrons and holes, has been one of the most actively studied topics on these two-dimensional semiconductors, where the excitons exhibit remarkably new features due to the strong Coulomb binding, the valley degeneracy of the band edges and the valley-dependent optical selection rules for interband transitions. Here, we give a brief overview of the experimental and theoretical indings on excitons in two-dimensional transition-metal dichalcogenides,with focus on the novel properties associated with their valley degrees of freedom.