Many theoretical efforts were made to understand the core and conal emission identified from observations by Rankin (1983) and Lyne and Manchester (1988). One of them, named as inverse Compton scattering (ICS) model (Qiao & Lin 1998), has been proposed. It is found in the model that: there are central or ‘core’ emission beam, and one or two hollow conical emission beams; the different emission components are emitted at different heights; owing to different radiation components emitted from different height, the observed emission beams can be shifted from each other due to retardation and aberration effects; the sizes of emission components change with frequencies. Recent developments of the model include: simulations of pulse profiles at different frequencies; studying the basic polarization properties of inverse Compton scattering in strong magnetic fields; computing the polarizations and spectrum of core and cones. A new classification system was also proposed. The main results calculated from the model are consistent with the observations.