Given an integral affine manifold one can easily produce a symplectic manifold fibered by Lagrangian tori. When the affine base has singularities of certain type, one should be able to obtain compact symplectic manifolds by means of gluing suitable singular fibres. In this lecture I will give models of Lagrangian fibrations which can be used to produce such compactifictions. These models resemble the singular behaviour expected to appear in ``generic" special Lagrangian fibrations, in particular, our models are given by piecewise smooth maps. This type of non-smoothness can be encoded into semi-global symplectic invariants.