  Ferromagnets are key materials for sensing and memory applications. In
contrast, antiferromagnets that represent the more common form of magnetically
ordered materials, have so far found less practical application beyond their
use for establishing reference magnetic orientations via exchange bias. This
might change in the future due to the recent progress in materials research and
discoveries of antiferromagnetic spintronic phenomena suitable for device
applications. Experimental demonstrations of the electrical switching and
electrical detection of the N\'eel order open a route towards memory devices
based on antiferromagnets. Apart from the radiation and magnetic-field
hardness, memory cells fabricated in antiferromagnets are inherently multilevel
which could be used for neuromorphic computing. Switching speeds attainable in
antiferromagnets far exceed those of the ferromagnetic and semiconductor memory
technologies. Here we review the recent progress in electronic spin-transport
and spin-torque phenomena in antiferromagnets that are dominantly of the
relativistic quantum mechanics origin. We discuss their utility in pure
antiferromagnetic or hybrid ferromagnetic/antiferromagnetic memory devices
