  With the arrival of the era of gravitational wave astronomy, the strong
gravitational field regime will be explored soon in various aspects. In this
article, we provide a general review over cylindrical systems in Einstein's
theory of general relativity. In particular, we first review the general
properties, both local and global, of several important solutions of Einstein's
field equations, including the Levi-Civita and Lewis solutions and their
extensions to include the cosmological constant and matter fields, and pay
particular attention to properties that represent the generic features of the
theory, such as the formation of the observed extragalactic jets and
gravitational Faraday rotation. We also review studies of cylindrical
wormholes, gravitational collapse and Hoop conjecture, and polarizations of
gravitational waves. In addition, by rigorously defining cylindrically
symmetric spacetimes, we clarify various (incorrect) claims existing in the
literature, regarding to the generality of such spacetimes.
