Axisymmetric magnetic mirrors are capable of confining high-β plasma and, at the same time, enable provision of higher magnetic field in the confinement region compared to non-axisymmetric systems. These advantages and their technical simplicity make them rather attractive as high-flux volumetric neutron sources, fission-fusion hybrids, and in the longer term as pure fusion reactors. The specific issues that still have to be further studied are plasma MHD stability at plasma parameters relevant to fusion applications, too-high plasma end losses, and the relatively low electron temperatures obtained so far in the experiments. These main physics issues were successfully addressed in the recent experiments in the GDT and GOL-3 devices in Novosibirsk. The review concludes with an update of the experimental results from both experimental devices and a discussion about the limiting factors in the current experiments. Specifically, we report on an almost twofold increase of the electron temperature with application of ECR heating, which was obtained in the experiments on the GDT device, and control of plasma rotation profile by injection of an electron beam at the end of the device, which was demonstrated in the GOL-3 device.