The optical microresonators reviewed in this paper are called bottle microresonators because their profile often resembles an elongated spheroid or a microscopic bottle. These resonators are commonly fabricated from an optical fiber by variation of its radius. Generally, variation of the bottle microresonator (BMR) radius along the fiber axis can be quite complex presenting, e.g., a series of coupled BMRs positioned along the fiber. Similar to optical spherical and toroidal microresonators, BMRs support whispering gallery modes (WGMs) which are localized inside the resonator due to the effect of total internal reflection. The elongation of BMRs along the fiber axis enables their several important properties and applications not possible to realize with other optical microresonators. The paper starts with the review of the BMR theory, which includes their spectral properties, slow WGM propagation along BMRs, theory of Surface Nanoscale Axial Photonics (SNAP) BMRs, theory of resonant transmission of light through BMR microresonators coupled to transverse waveguides (microfibers), theory of nonstationary WGMs in BMRs, and theory of nonlinear BMRs. Next, the fabrication methods of BMRs including melting of optical fibers, fiber annealing in SNAP technology, rolling of semiconductor bilayers, solidifying of a UV-curable adhesive, and others are reviewed. Finally, the applications of BMRs which either have been demonstrated or feasible in the nearest future are considered. These applications include miniature BMR delay lines, BMR lasers, nonlinear BMRs, optomechanical BMRs, BMR for quantum processing, and BMR sensors.