Analytic Approaches to Understanding the Distribution and Evolution of Intracluster Gas

I will briefly review various analytic approaches to understanding the contents and properties of the hot X-ray emitting gas contained in clusters and groups. Special emphases are given to the following three issues: (1)Reconstruction of the gas distribution in groups and clusters from a (joint) analysis of X-ray, SZ and gravitational lensing observations; (2)Test of the analytic density profiles of dark halos suggested by numerical simulations and empirical models with current X-ray data; And (3)the effects of preheating and radiative cooling on the X-ray properties of groups and clusters.