This article reviews recent progress towards the design of near-field flat focusing mirrors, focusing/imaging light patterns in reflection. An important feature of such flat focusing mirrors is their transverse invariance, as they do not possess any optical axis. We start with a review of the physical background to the different focusing mechanisms of near- and far-field focusing. These near-field focusing devices like flat lenses and the reviewed near-field focusing mirrors can implement planar focusing devices without any optical axis. In contrast, various types of far-field planar focusing devices, such as high-contrast gratings and metasurfaces, unavoidably break the transverse invariance due to their radially symmetrical structures. The particular realizations of near-field flat focusing mirrors including Bragg-like dielectric mirrors and dielectric subwavelength gratings are the main subjects of the review. The first flat focusing mirror was demonstrated with a chirped mirror and was shown to manage an angular dispersion for beam focusing, similar to the management of chromatic dispersion for pulse compression. Furthermore, the reviewed optimized chirped mirror demonstrated a long near-field focal length, hardly achieved by a flat lens or a planar hyperlens. Two more different configurations of dielectric subwavelength gratings that focus a light beam at normal or oblique incidence are also reviewed. We also summarize and compare focusing performance, limitations, and future perspectives between the reviewed flat focusing mirrors and other planar focusing devices including a flat lens with a negative-index material, a planar hyperlens, a high-contrast grating, and a metasurface.