While artificial intelligence, capable of readily addressing cognitive tasks, has transformed technologies and daily lives, there remains a huge gap with biological systems in terms of performance per energy unit. Neuromorphic computing, in which hardware with alternative architectures, circuits, devices, and/or materials is explored, is expected to reduce the gap. Antiferromagnetic spintronics could offer a promising platform for this scheme. Active functionalities of antiferromagnetic systems have been demonstrated recently and several works indicated their potential for biologically inspired computing. In this perspective, we look through the prism of these works and discuss prospects and challenges of antiferromagnetic spintronics for neuromorphic computing. Overview and discussion are given on non-spiking artificial neural networks, spiking neural networks, and reservoir computing.