Total-reflection mirror devices for X-ray free-electron laser focusing are discussed in terms of optical design, mirror-fabrication technology, a wavefront diagnosis method and radiation-damage testing, as a review of the present status of the focusing optics at the SPring-8 angstrom compact free-electron laser (SACLA). Designed beam sizes of 1 µm and 50 nm, and spot sizes almost matching prediction have been achieved and used to explore topics at the forefront of natural science. The feasibility of these devices is determined to be sufficient for long-term and stable operation at SACLA by investigating the radiation-damage threshold and achievable accuracies in the mirror figure and alignment.