Gamma-ray bursts (GRBs) are extremely energetic explosions at cosmological distances. We have made great progress in understanding the mysteries of these events since they were discovered more than forty years ago. However, some open questions still remain, e.g. how many classes of GRBs are there, what are the progenitors of these classes, and what is the central engine powering these huge explosions? Thanks to the NASA missions Swift and Fermi, which are used to detect the multi-wavelength emission from these transients, our understanding of GRBs has been greatly advanced. In this dissertation, I use multi-wavelength data to constrain the progenitor and central engine of GRBs. My dissertation consists of three parts: (1) By adding the third dimension ``amplitude'' as a complementary criterion in classifying GRBs, we test whether some short GRBs are ``tip-of-iceberg'' of long GRBs, and explain why some high redshift long GRBs have short durations in the rest frame. (2) Using Swift data, we investigate whether the data are consistent with the hypothesis that there exist millisecond magnetar central engines in some long GRBs. We reach the conclusion that at least some long GRBs have a magnetar central engine. (3) We test how well the data are consistent with the magnetar central engine model for short GRBs. We identify that a good fraction of short GRBs have a supra-massive magnetar central engine, which collapses to a black hole after hundreds of seconds. We use the data to constrain the neutron star equation of state.
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