This talk presents and discusses advanced neural networks by focusing on complex valued neural networks CVNNs and their applications in the remote sensing and imaging fields. CVNNs are suitable for adaptive processing of complex amplitude information. Since active remote sensing deals with coherent electromagnetic wave, we can expect CVNNs to work more effectively than conventional neural networks or other adaptive methods in real number space. Quaternion or Hypercomplex valued neural networks are also discussed in relation to polarization information processing. The beginning half of the Talk is devoted to presentation of the basic idea, overall framework, and fundamental treatment in the CVNNs. We discuss the processing dynamics of Hebbian rule, backpropagation learning, and self-organizing map in the complex domain. The latter half shows some examples of CVNN processing in the geoscience and remote sensing society GRSS fields. Namely, we present distortion reduction in phase unwrapping to generate digital elevation model DEM from the data obtained by interferometric synthetic aperture radar InSAR. In polarization SAR, we apply quaternion networks for adaptive classification. Another example is ground penetrating radar GPR to visualize underground objects to distinguish specific targets in high clutter situation. Finally we discuss the prospect of the CVNNs in the GRSS fields.