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, along with other – being generic CI methods 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, geneinspired and quantum inspired CI. The main contribution of the chapter though is the introduction of methods inspired by the integration of principles from several levels of information processing, namely: (1) a computational neurogenetic model, that combines in one model gene information related to spiking neuronal activities; (2) a general framework of a quantum spiking neural network model; (3) a general framework of a quantum computational neuro-genetic model. Many open questions and challenges are discussed, along with directions for further research.