In this talk, I shall discuss the multiple exciton states observed in the monolayers of transition-metal dichalcogenides. These near-two-dimensional exciton states are markedly different from typical exciton states observed in three-dimensional bulk semiconductors and their quantum wells, in terms of binding energy and spontaneous emission rate. This makes these monolayers an ideal platform to study exciton physics. With an increase in the number of layers, the band structure is modified significantly, modulating the exciton states and giving rise to unique layer degree of freedom of excitons. Monolayers being atomically thin, these exciton states can be manipulated by the surrounding dielectric environment. The implications of charge and energy transfer in vertical layered heterojunction will be discussed.