A review is presented of the state-of-the-art in theory and experiment of microwave magnetically insulated linear oscillators (MILO). This paper includes the following problems: the Brillouin electron flow formation in coaxial magnetically insulated transmission lines (MITL), electromagnetic waves and instabilities in coaxial smooth-wall transmission lines (TL), microwave dispersion theory in coaxial slow-wave periodic structures, linear theory and computer simulations of the processes of microwave generation by the Brillouin electron flow in coaxial slow-wave structures. Major results are also given in experimental studies on microwave MILOs.