  We study the notion of orderability of isotopy classes of Legendrian
submanifolds and their universal covers, with some weaker results concerning
spaces of contactomorphisms. Our main result is that orderability is equivalent
to the existence of spectral selectors analogous to the spectral invariants
coming from Lagrangian Floer Homology. A direct application is the existence of
Reeb chords between any closed Legendrian submanifolds of a same orderable
isotopy class. Other applications concern the Sandon conjecture, the Arnold
chord conjecture, Legendrian interlinking, the existence of time-functions and
the study of metrics due to Hofer-Chekanov-Shelukhin, Colin-Sandon,
Fraser-Polterovich-Rosen and Nakamura.
