The classical Noether-Lefschetz theorem says that any curve in a very general surface X in the projective space of degree greater than 4 is a restriction of a surface in the ambient space, namely the Picard number of X is 1. The Noether- Lefschetz locus is the locus where the Picard number is greater than 1. Green and Voisin give an estimate on the codimension of these loci. We study quasi-smooth surfaces in toric orbifolds, generalize the Noether- Lefschetz theorem, define the Noether-Lefschetz loci, and study its properties. (In collaboration with U. Bruzzo.) I will also discuss related open problems.