This article reviews recent advances in graphene-based materials and devices for terahertz science and technology. The fundamental basis of the optoelectronic properties of graphene is first introduced. Then the synthesis and crystallographic characterization of graphene materials, particularly focused on the authors' original heteroepitaxial graphene-on-silicon technology, are briefly described. Then nonequilibrium carrier relaxation and recombination dynamics in optically or electrically pumped graphene is discussed to introduce the possibility of negative dynamic conductivity toward the creation of graphene terahertz lasers. Unique terahertz dynamics of the two-dimensional plasmons in graphene are also addressed.