Here we present an analysis of the current state in the field of development of hardware accelerators of artificial intelligence (AI). Despite the fairly good progress made over the past decades, this area is experiencing a number of significant difficulties in its development. The solution to this problem lies in the application of new approaches to the organization of computing, in particular, computing in memory enabled by nanoelectronic memristive devices. We provide an overview of state-of-art systems, as well as our own version of the experimental concept of AI accelerators based on metal-oxide memristive devices and the massively parallel architecture for information processing.