  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.
