This paper reviews recent advances in terahertz-wave generation in graphene toward the creation of new types of graphene terahertz lasers. Fundamental basis of the optoelectronic properties of graphene is first introduced. Second, nonequilibrium carrier relaxation/recombination dynamics and resultant negative terahertz conductivity in optically or electrically pumped graphene are described. 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 discussed. Finally, the advantages of graphene materials and devices for terahertz-wave generation are summarized.