Theoretical and experimental results on excitonic effects in monomolecular layers of transition metal dichalcogenides are reviewed. These two-dimensional semiconductors exhibit a direct bandgap of about 2 eV at the Brillouin zone edges, and the binding energies of their neutral and charged excitons are in the range of hundreds and tens of millielectron-volts, respectively. This implies that electron±hole complexes determine the optical properties of transition metal dichalco-genide monolayers. Topics discussed in this review include the band structure details needed to understand the excitonic effects in these materials, the structure and fine structure of exciton and trion energy levels, the features of the spin and valley dynamics of Coulomb complexes, and how neutral and charged excitons manifest themselves in linear and nonlinear optical effects.