In this talk,I will discuss absorbing interface conditions,which were proposed either at interfaces between different physical models or the same model with different discretization schemes.The proposed interface conditions permit two-way transmission of low frequency waves across interfaces which can be supported by both models and perform one-way absorption of high frequency waves which can only be supported by fine models when they travel from fine mesh regions to coarse ones.Numerical examples are presented to illustrate the efficiency of the proposed absorbing interface conditions.