The document summarizes recent advances in analytical models for electromagnetic scattering from rough surfaces, including the statistical integral equation method (SIEM) and the extended advanced integral equation method (E-AIEM). SIEM incorporates surface slope statistics into the Kirchhoff approximation to improve accuracy. E-AIEM makes fewer assumptions than previous models and includes correction terms involving the error function for more accurate cross and complementary scattering coefficients, especially when surfaces or media are lossy. Testing shows these new methods agree well with full-wave simulations and experimental data.