This thesis focuses on the analytical and numerical studies of the gamma-ray burst (GRB) afterglows. Since its discovery in 1997, it has been believed that GRB afterglow is emitted by the forward shock (FS) wave sweeping up the ambient medium. However, recent observations of early afterglows made by the Swift satellite revealed unexpected features such as early X-ray plateaus and peculiar chromatic breaks in the afterglow lightcurves. It appears that these new observations are not consistent with the standard picture of afterglow production by the FS wave. Together with the FS sweeping up the ambient medium, a reverse shock (RS) is expected in the burst ejecta. The RS was previously studied only under simplifying assumptions; for instance, an equal pressure at the FS and RS, or a constant ratio of the two pressures was assumed. In this thesis, we find that these simplifying assumptions are inconsistent with the energy conservation law in the expanding blast wave. Then, we develop a consistent mechanical model for a general problem of explosions driven by ejecta with arbitrary stratification. The mechanical model allows us to realize the existence of a new class of models with rapid and strong evolution of the RS. An exploration of the RS dynamics suggests that the RS emission could naturally provide a solution to the current crisis of afterglow theory posed by the Swift. Thus, we propose a new model in which the entire afterglow is emitted by a long-lived RS in the burst ejecta, and the FS propagates invisible. This model implies that the observed afterglow may be used as a direct probe of the ejecta. In particular, we present a model where the ejecta made of a fast head and slow tail naturally reproduces the observed X-ray plateaus and chromatic breaks in the RS emission.