The Hull-Strominger system is a system of nonlinear PDEs describing the geometry of compactification of heterotic strings with flux to 4d Minkowski spacetime, which can be regarded as a generalization of Ricci-flat Kahler metrics coupled with Hermitian Yang-Mills equation on non-Kahler Calabi-Yau 3-folds. In this talk, we present an explicit construction of smooth solutions to the Hull-Strominger system with infinitely many topological types and sets of Hodge numbers, thus showing that there may be infinitely many candidates in the string theory landscape when flux is present.