Low energy models of string theory

Abstract: 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.