Abstract: The theoretical limitation of the classical computing machinery, including all the computers with von Neumann architecture, was defined by Alan Turing in 1936. Owing to lack of the hardware neuromorphic devices, neural networks have been implemented with computers to realize artificial intelligence for decades. However, the von Neumann architecture doesn’t match with the asynchronous parallel structure and communication mechanism of the neural networks, with consequences such as huge power consumption. To develop the neural network oriented architecture for artificial intelligence and common information processing is an important direction for architecture research. Brain-like machine is an intelligent machine which is constructed with neuromorphic devices according to the structure of biological neural network, and is better on spatio-temporal information processing than classic computer. The idea of brain-like machine had been proposed before the invention of computer. The research and development practice has been carried out for more than three decades. As one of the several brain-like systems being in operation, SpiNNaker focuses on the research on the architecture of brain-like systems with an effective brain-like scheme. In the next 20 years or so, it is expected that the detailed analysis of model animal brain and human brain will be completed step by step, and the neuromorphic devices and integrated processes will be gradually mature, and the brain-like machine with structure close to the brain and performance far beyond the brain is expected to be realized. As a kind of spiking neural networks, and with neuromorphic devices which behavior is true random, the brain-like machine can emerge abundant nonlinear dynamic behaviors. It had been proven that any Turing machine can be constructed with spiking neural network. Whether the brain-like machine can transcend the theoretical limitation of the Turing machine? This is a big open problem to break through.