The discovery of multiband afterglows definitely shows that most γ-ray bursts are of cosmological origin. γ-ray bursts are found to be one of the most violent explosive phenomena in the Universe, in which astonishing ultra-relativistic motions are involved.In this article, the multiband observational characteristics of γ-ray bursts and their afterglows are briefly reviewed. The standard model of γ-ray bursts, i.e. the fireball model, is described. Emphasis is then put on the importance of the nonrelativistic phase of afterglows. The concept of deep Newtonian phase is elaborated. A generic dynamical model applicable in both the relativistic and nonrelativistic phases is introduced. Based on these elaborations, the overall afterglow behaviors, from the very early stages to the very late stages, can be conveniently calculated.