||We give a survey of the focusing energy-critical inhomogeneous nonlinear Schr\"odinger equation(NLS). The cubic NLS can be a physical model of dilute Bose-Einstein condensate when the two-body interation of the condensate are considered. The global well-posedness(GWP) of energy-critical homogeneous NLS is well-known for the results of Kenig and merle in 2006. In this talk we will show the GWP, scattering results for radial solutions to energy-critical inhomogeneous NLS and blowup results for the radial solutions solutions under some energy conditions related to stationary problem of homogeneous NLS. We also show the nonexistence of positive radial solution to critical stationary problem of the inhomogeneous NLS. nhomogeneous coefficient index $b$ can be extended to $\frac32$ via weighted space. This talk is based on co-work with Yonggeun Cho and Seokchang Hong.