Abstract: Strong approximation theorems are ubiquitous in arithmetic geometry and have been broadly studied over global fields. But what happens if the base field is replaced by the function field of a complex algebraic curve? This question has been tackled since the last decade, using the deformation theory of algebraic curves. In this presentation, we shall give some generalities on strong approximation for varieties over $\mathbf{C}(t)$ and discuss the remanence of this property on the complementary of any closed subset of codimension 2.