  String theory is the prime candidate for the theory of everything. However,
it must be defined in ten dimensions to be consistent. To get 4D physics, the 6
other dimensions should be curled up in a small compact manifold, this
procedure is called string compactification. In this review, we will review
different compactification schemes proving that in absence of flux, the compact
manifold must be a Calabi-Yau manifold. Then, we review compactifications with
flux using generalized complex geometry. We then discuss some applications in
cosmology like the swampland project and the cosmological models derived from
it. We then discuss non relativistic string theories and introduce a toroidal
compactifications for such theories. Finally, we discuss some open questions in
the field.
