  We derive constraints on Lagrangian concordances from Legendrian submanifolds
of the standard contact sphere admitting exact Lagrangian fillings. More
precisely, we show that such a concordance induces an isomorphism on the level
of bilinearised Legendrian contact cohomology. This is used to prove the
existence of non-invertible exact Lagrangian concordances in all dimensions. In
addition, using a result of Eliashberg-Polterovich, we completely classify
exact Lagrangian concordances from the Legendrian unknot to itself in the tight
contact-three sphere: every such concordance is the trace of a Legendrian
isotopy. We also discuss a high dimensional topological result related to this
classification.
