This chapter discusses opportunities and challenges for the creation of methods of computational intelligence (CI) and more specifically – artificial neural networks (ANN), inspired by principles at different levels of information processing in the brain: cognitive, neuronal, genetic, and quantum, and mainly, the issues related to the integration of these principles into more powerful and accurate CI methods. It is demonstrated how some of these methods can be applied to model biological processes and to improve our understanding in the subject area; generic CI methods being applicable to challenging generic AI problems. The chapter first offers a brief presentation of some principles of information processing at different levels of the brain and then presents brain inspired, gene inspired, and quantum inspired CI. The main contribution of the chapter, however, is the introduction of methods inspired by the integration of principles from several levels of information processing, namely: A computational neurogenetic model that in one model combines gene information related to spiking neuronal activities. A general framework of a quantum spiking neural network (SNN) model. A general framework of a quantum computational neurogenetic model (CNGM). Many open questions and challenges are discussed, along with directions for further research.