We are interested in understanding when a given Fano variety can be realised as a fibre of a Mori fibre space. We are able to provide two criteria, one sufficient and one necessary, which turn into a characterisation in the rigid case. In this talk we will also show how our criteria can be used to give a complete answer in the case of surfaces, an almost complete picture for 3folds and a combinatorial characterisation on the polytope in the toric case. This talk is based on a joint work with Giulio Codogni, Roberto Svaldi and Luca Tasin.