  The detection of optical re-brightenings and X-ray plateaus in the afterglows
of gamma-ray bursts (GRBs) challenges the generic external shock model.
Recently, we have developed a numerical method to calculate the dynamic of the
system consisting of a forward shock and a reverse shock. Here, we briefly
review the applications of this method in the afterglow theory. By relating
these diverse features to the central engines of GRBs, we find that the steep
optical re-brightenings would be caused by the fall-back accretion of black
holes, while the shallow optical re-brightenings are the consequence of the
injection of the electron-positron-pair wind from the central magnetar. These
studies provide useful ways to probe the characteristics of GRB central
engines.
