Certain simple symplectic manifolds (symplectic vector space, Milnor fibres of certain complex surface singularities,...) contain sets of symplectically distinct Lagrangian tori which have the following remarkable property: they remain symplectically distinct under embeddings into any reasonable (i.e. geometrically bounded) symplectic manifold. This leads to a vast extension of the class of spaces in which the existence of exotic tori is known, especially in dimensions six and above. In this talk we mainly focus on recent joint work with Johannes Hauber and Joel Schmitz which treats the more intricate case of dimension four.