In this paper recent advances in terahertz-wave generation in graphene are reviewed. First, fundamental basis of the optoelectronic properties of graphene is introduced. Second, nonequilibrium carrier relaxation and recombination dynamics in optically or electrically pumped graphene is described to introduce a possibility of negative dynamic conductivity in a wide terahertz range. Third, recent theoretical advances toward the creation of current-injection graphene terahertz lasers are described. Fourth, unique terahertz dynamics of the two-dimensional plasmons in graphene are described. Finally, the advantages of graphene materials and devices for terahertz-wave generation are summarized.