Cosmic Gamma-ray Bursts and their afterglows are the most
  luminous stellar events in the Universe, and they are potentially
  promising probes for cosmology. In this talk I report our understanding to
  the nature of these events with multi-wavelength observations, focusing on
  both spectral and temporal properties and their possible physical
  implications as well. I also discuss the spectrum-energy relations of GRBs
  and their application in cosmography. The outline of my talk is as follow:
  (1) Introduction to GRB observations and the fireball models; (2) GRB
  populations and challenges from Swift observations; (3) Swift X-ray
  telescope observations and challenges to conventional GRB models; (4) GRB
  spectrum-energy relations and GRB cosmography.