Coronal heating is an important problem in solar physics. With the development of highly qualified instruments, such as TRACE, SOHO and Yohkoh, more and more observations about coronal loops have been obtained. The coronal loops' heating, being an important ingredient of coronal heating, has been paid particular attentions recently. But there are still some key issues about the structure and mechanism of the loops' heating unresolved. In this paper, after a brief review on the latest progress in both observations and modeling of coronal loops, we emphatically discuss the heating of hydrostatic loops and hydrodynamic loops based on the 1D model. The prospect of the subject is presented.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html