Computational electromagnetics (EM) as well as multiphysics (MP) methods remain very challenging tasks even with nowadays. This talk will give a brief outline from CEM to CMP. Further, their applications for solving various complex electromagnetic environmental effect problems will be addressed. In particular, main challenges in the development of MP algorithm will be indicated and key strategies for attacking them will also be demonstrated. This talk is provided for both research engineers and scientists who are active in CEM/MP studies and applications.