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One of the main properties of human intelligence is that it is evolving (developing, revealing, unfolding) based on: (1) Genetically "wired" rules; (2) Experience and learning during life time. The paper argues that we need to understand how the brain operates at its different levels of information processing and then use some of these principles "when building intelligent machines. Without "drowning" into the sea of details, some main principles of information processing in the brain at cognitive-, neuronal-, genetic-, and particle field information levels are reviewed. The paper takes the approach towards understanding and building integrative connectionist systems, that integrate principles and rules from different hierarchical levels of information processing in their dynamic interaction, as an approach to develop intelligent machines. Examples given include: simple evolving connectionist systems; evolving spiking neural networks; integrative neurogenetic models; genetically defined robots; quantum evolutionary algorithms for exponentially faster optimization; integrative quantum neural networks. Some of the new integrative models are significantly faster in feature selection and learning and can be used to solve efficiently NP complete biological and engineering problems for adaptive, incremental learning in a large dimensional space-an important feature of the human intelligence. They can also help to better understand complex information processes in the brain, especially how information processes at different information levels interact to achieve a higher level intelligent human behavior. Open questions, challenges and directions for further research are presented.