The SYZ conjecture predicts that for polarised Calabi-Yau manifolds undergoing the large complex structure limit, there should be a special Lagrangian torus fibration. A weak version asks if this fibration can be found in the generic region. I will discuss my recent work proving this weak SYZ conjecture for the degenerating hypersurfaces in the Fermat family. Although these examples are quite special, this is the first construction of generic SYZ fibrations that works uniformly in all complex dimensions.