  Finding methods for the most efficient and fastest detection and control of
magnetic domains in antiferromagnets is presently among the main challenges of
magnetic research at large. We analyse the problem of optical read-out and
control of the antiferromagnetic Neel vector using symmetry analysis and the
principles of equilibrium thermodynamics. Following the pioneering approach of
Dzyaloshinksii, we divide all antiferromagnets in three classes. It is shown
that, using the magneto-optical Faraday effect or other effects which scale
linearly with the antiferromagnetic Neel vector, it is possible to distinguish
antiferromagnetic domains with mutually opposite N\'eel vectors in two of the
three classes. Symmetry properties of one of these two classes are similar to
those of altermagnets. The analysis also reveals multiple mechanisms to
directly excite spins with light for practically every type of antiferromagnet.
