We present a complete overview of the computational power of recurrent neural networks involved in an interactive bio-inspired computational paradigm. More precisely, we recall the results stating that interactive rational- and realweighted neural networks are Turing-equivalent and super-Turing, respectively.We further prove that interactive evolving neural networks are super-Turing, irrespective of whether their synaptic weights are modeled by rational or real numbers. These results show that the computational powers of neural nets involved in a classical or in an interactive computational framework follow similar patterns of characterization. They suggest that some intrinsic computational capabilities of the brain might lie beyond the scope of Turing-equivalent models of computation, hence surpass the potentialities every current standard artificial models of computation.