  As of today there exist consistent, gauge-invariant string field theories
describing all string theories: bosonic open and closed strings, open
superstrings, heterotic strings and type II strings. The construction of these
theories require algebraic ingredients, such as $A_\infty$ and $L_\infty$
homotopy algebras, geometric ingredients, relevant to the building of moduli
spaces of Riemann surfaces and the distribution of picture changing operators,
and field-theoretic ingredients, involving two-dimensional CFT's and BCFT's and
Batalin-Vilkovisky quantization. Applications of string field theory include
the description of non-perturbative phenomena such as tachyon condensation and
classical solutions, and the resolution of a number of ambiguities that bedevil
the world-sheet formulation of perturbative string theory. It also allows,
given a proper definition of contours of integration for momenta, for a proof
of unitarity and a clear understanding of the ultraviolet finiteness of the
theory. In this article we review these developments.
